Add the sourdough starter, whole milk, bread flour, eggs, salt, maple syrup, and vanilla extract to the bowl of a stand mixer fitted with a dough hook. Mix on low speed until the ingredients come together and no dry flour remains.

With the mixer running, add the softened butter 1 tablespoon at a time, allowing each addition to become mostly incorporated before adding the next.

Once all the butter has been added, knead for approximately 7 minutes on medium-high, provided that speed is appropriate for kneading with your mixer. The dough should become smooth, elastic, and slightly tacky. It should begin pulling away from the sides of the bowl, although it may still cling slightly to the bottom.

Transfer the dough to a lightly greased bowl or straight-sided container. Cover to prevent the surface from drying out. Mark the starting dough level if using a clear, straight-sided container so you can easily track its growth.

Let the dough ferment at room temperature until it has risen by approximately 50%. This may take 6–10 hours, depending on your kitchen temperature and the strength of your starter. Watch the dough, not the clock.

During bulk fermentation, the sourdough culture produces gas that gradually expands and lightens the dough. Look for a noticeably puffier appearance, a slightly domed surface, and small bubbles along the sides or bottom of the container. The dough may jiggle gently when the container is moved. It does not need to double in size.

Once the dough has risen by approximately 50%, cover tightly and refrigerate overnight, or continue directly to shaping. Refrigerating makes the buttery dough firmer and easier to roll and braid.

In a small bowl, mix the softened butter, brown sugar, and cinnamon until evenly combined into a spreadable paste.

Lightly flour your work surface. Roll the dough into a rectangle measuring approximately 12 × 16 inches (30 × 41 cm).

Spread the cinnamon filling evenly over the dough, reaching close to the edges.

Position the rectangle with one of the shorter, 12-inch ends facing you. Fold the far short end down over the middle third of the dough. Then fold the near short end up over that layer, like folding a letter. You should have a three-layer rectangle measuring approximately 12 × 5⅓ inches.

Position the folded rectangle with its 12-inch side facing you. Use a bench scraper to divide that length in half, cutting through all the layers. Cut each half in half again to create four equal sections.

Cut each quarter into thirds to make 12 strips total. Each strip should measure approximately 1 inch wide and 5⅓ inches long.

Working with one strip at a time, make two lengthwise cuts to create three connected strands. Leave approximately ½ inch intact at the top so the strands stay attached.

Gently separate the strands. Cross the right strand over the center strand, then cross the left strand over the new center strand. Continue alternating right and left over the center until you reach the bottom. Braid gently without pulling the dough too tightly.

Pinch the bottom ends together to secure the braid.

Starting at the intact top, roll the braid over itself toward the pinched end to form a knot. Tuck the tail underneath to help hold its shape.

Place the knot in a greased 9 × 13-inch baking pan. Repeat with the remaining strips, arranging the knots evenly in the pan.

Cover the pan with lightly greased plastic wrap and let the knots rise at room temperature for approximately 1–3 hours. Dough shaped straight from the refrigerator or rising in a cool kitchen may need longer.

Look for knots that are noticeably fuller, soft, and puffy, with less space between them. Gently press a doughy area with a lightly floured fingertip. The indentation should slowly spring back while leaving a slight impression. If it springs back immediately, allow more rising time.

Near the end of the second rise, preheat the oven to 350°F (177°C).

Remove the plastic wrap and bake for approximately 25 minutes, or until the knots are golden brown and baked through. Check the dough in a center knot with an instant-read thermometer, avoiding the filling. The internal temperature should be 190–200°F (88–93°C).

Let the knots cool in the pan for 10–15 minutes before adding the frosting.

Add additional milk a little at a time, if needed, until the frosting reaches your desired spreading or drizzling consistency.

Spread or drizzle the frosting over the warm knots. Serve warm!