Sourdough Lemon Curd Cream Cheese Buns

If you want to make the lemon curd from scratch, follow these instructions (I recommend making it the day or two before so it can cool and thicken--it keeps well in the fridge).
In a medium saucepan, whisk together the eggs, sugar, and melted butter.
Add the lemon juice and cook over low-medium heat, whisking continuously. As the mixture heats, small bubbles will form.
Keep whisking constantly until the curd thickens, about 7-10 minutes. Once thickened, remove from heat and let it cool completely before using.
Store in an airtight container in the refrigerator for up to 1-2 weeks.

In a small bowl or jar, combine the sourdough starter, flour, and filtered water.
Mix until fully combined and no dry flour remains.
Cover loosely and allow to rest at room temperature for 6–10 hours, or until doubled in size, bubbly, and active.
The levain is ready when it has peaked and the top looks slightly domed or just begins to flatten.

In the bowl of a stand mixer fitted with the dough hook, add the active levain/sourdough starter, warm milk, flour, eggs, salt, sugar, and vanilla extract.
Mix on low to medium speed until a shaggy dough forms.
With the mixer running, add the softened butter one tablespoon at a time, allowing each piece to fully incorporate before adding more. Scrape down the bowl as needed.
Increase the mixer speed to medium-high and knead for 7–10 minutes, or until the dough becomes smooth, elastic, and begins pulling away from the sides of the bowl.
Brioche dough is naturally soft, wet, and sticky. It may be tempting to add extra flour, but avoid doing so for the softest texture.
Cover the bowl and allow the dough to rise at room temperature for 6–10 hours, or until increased in size by about 30–50%. Once it's fermented, you can continue on to shaping the buns or cover and let chill in the fridge overnight.
Depending on the temperature of your home, this rise may take longer. In cooler kitchens, expect closer to 12 hours. Watch the dough, not the clock.

Line two baking sheets with parchment paper.
Turn the dough onto a lightly floured surface and divide into 10 equal portions, about 95–100 g each.
Shape each piece into a smooth ball and place onto the prepared baking sheets, leaving space between each bun.
Cover loosely with greased plastic wrap and let the buns complete their second rise, which will take about 1-4 hours depending on the temperature of your kitchen. If you chilled the dough overnight, it will be closer to the 3-4 hour mark.

Cream Cheese Filling
In a medium bowl, use a hand mixer to beat the softened cream cheese and vanilla extract until smooth and creamy.
Add the powdered sugar and mix until fully combined and fluffy.
Lemon Curd
Stir the lemon curd until smooth and easily spoonable, if needed.

Preheat the oven to 350°F (175°C).
Using your fingers or the bottom of a glass, gently press an indentation into the center of each dough ball.
Spoon about 2 tablespoons of cream cheese filling into the center of each bun.
Top with about 2 tablespoons of lemon curd.
Brush the outer edges of each bun with the whisked egg and milk.

In a small bowl, whisk together the powdered sugar, vanilla extract, and milk until smooth.
Adjust the milk as needed until your desired consistency is reached.
Drizzle over the warm buns before serving.

Storage Instructions