In the bowl of a stand mixer fitted with the dough hook, add the active sourdough starter, warm milk, all-purpose flour, eggs, salt, granulated sugar, and vanilla extract.

Mix on low to medium speed until a shaggy dough forms and the ingredients are mostly incorporated.

With the mixer running, add the softened butter one tablespoon at a time, allowing each addition to fully incorporate before adding the next. Scrape down the sides and bottom of the bowl as needed.

Once all the butter has been incorporated, increase the mixer to medium-high speed and knead for about 7–10 minutes, or until the dough is smooth, elastic, and begins pulling away from the sides of the bowl.

The dough will be soft, rich, and somewhat sticky. Do not add extra flour simply because the dough feels sticky. Brioche dough is naturally soft, and adding too much flour can result in dense, dry kolaches.

Cover the bowl and allow the dough to ferment at room temperature for 6–10 hours, or until it has increased in volume by roughly 30–50%.

The exact fermentation time will depend on the temperature of your kitchen and the strength of your sourdough starter. In a cooler kitchen, the dough may take closer to 10–12 hours. Watch the dough rather than relying strictly on the clock.

Optional overnight fermentation: Once the dough has completed its bulk fermentation, cover it and refrigerate overnight. Chilled dough is easier to work with and can be shaped the following day.

Line two baking sheets with parchment paper.

Turn the fermented dough onto a lightly floured surface and divide it into 10 equal portions, approximately 90–100 g each.

Shape each portion into a smooth ball by gently pulling the edges of the dough toward the center and rolling it against the work surface to create surface tension.

Place the dough balls onto the prepared baking sheets, leaving several inches between each one.

Cover loosely with greased plastic wrap and allow the kolaches to complete their second rise for approximately 1–3 hours, depending on the temperature of your kitchen.

If the dough was refrigerated overnight, expect the second rise to take closer to 3 hours.

While the dough is completing its second rise, prepare all of the fillings and toppings.

In a medium bowl, beat the softened cream cheese until smooth.

Add the powdered sugar and vanilla extract and mix until completely smooth and creamy.

Set aside at room temperature while you prepare the remaining fillings.

Peel, core, and dice the apples into small, bite-sized pieces.

Add the diced apples, brown sugar, cinnamon, ginger, vanilla extract, and 1/4 cup water to a medium saucepan.

Cook over medium heat, stirring occasionally, until the apples begin to soften and the mixture becomes syrupy, about 8–12 minutes.

In a small bowl, whisk together the cornstarch and 2 tablespoons water until completely smooth.

Slowly pour the cornstarch slurry into the cooked apples while stirring continuously.

Continue cooking for another 1–2 minutes, stirring constantly, until the apple mixture thickens and becomes glossy.

Remove from the heat and allow the filling to cool. It should be thick enough to mound onto the kolaches rather than run off the dough.

In a small bowl, combine the melted butter, flour, and brown sugar.

Stir with a fork until the mixture forms coarse crumbs.

Set aside.

If using store-bought caramel sauce, simply set it aside until the kolaches are baked and ready to serve.

For homemade caramel, add the brown sugar, heavy cream, butter, and salt, if using, to a medium saucepan.

Cook over medium heat, whisking frequently, for 5–8 minutes, allowing the mixture to gently bubble and thicken.

Once the caramel has thickened, remove the saucepan from the heat and stir in the vanilla extract.

Cook for another 1–2 minutes, then remove from the heat.

Allow the caramel to cool in the pan. It will continue to thicken as it cools.

Preheat the oven to 350°F (175°C).

Prepare the egg wash by whisking together the egg and milk.

Once the dough balls have completed their second rise, gently press down into the center of each one with your fingers or the bottom of a small glass, creating a deep well while leaving a raised border around the edges.

Be careful not to completely flatten the dough.

Brush the exposed dough lightly with the egg wash.

Add a generous spoonful of cream cheese filling to the center of each kolache.

Top with a spoonful of the cooled caramel apple filling.

Finish each kolache with a generous sprinkling of crumble topping.

Bake the kolaches at 350°F (175°C) for 25–30 minutes, or until the brioche is golden brown and baked through.

If you're baking both pans at the same time, rotate the baking sheets halfway through baking so the kolaches bake evenly.

Keep an eye on them toward the end of baking. The exact baking time will depend on the size of your kolaches and your oven.

Allow the kolaches to cool on the baking sheets for several minutes.

Once they are warm but no longer piping hot, drizzle generously with the caramel sauce.

Serve warm or at room temperature.