In a large mixing bowl (or the bowl of a stand mixer), combine the sourdough discard, all-purpose flour, granulated sugar, instant yeast (if using), and salt. Whisk briefly to combine.

Add the warm milk, melted butter, and egg. Mix with a spoon or your stand mixer with the dough hook attachment on low speed until a shaggy dough forms. If mixing by hand, turn the dough out onto a lightly floured surface.

Knead the dough for 8-10 minutes, either by hand or with the stand mixer on medium speed, until it becomes smooth, elastic, and passes the windowpane test (you can stretch a small piece thin enough to see light through it without tearing).

Lightly grease a clean large bowl with a little oil. Place the dough in the bowl, turning once to coat. Cover the bowl with plastic wrap or a damp kitchen towel and let it rise in a warm place for 1.5 to 2.5 hours, or until roughly doubled in size. (If not using yeast, this rise can take 4-6 hours, or even longer depending on the strength of your discard and ambient temperature).

While the dough is rising, prepare the cinnamon filling: In a small bowl, combine the brown sugar and ground cinnamon. Stir well to mix. Melt the 2 tablespoons of butter for the filling and set aside.

Once the dough has risen, gently punch it down to release the air. Turn it out onto a lightly floured surface. Roll the dough into a rectangle, approximately 14x10 inches (35x25 cm).

Brush the melted butter evenly over the entire surface of the dough, leaving about a 1/2-inch border clean on one long edge. Sprinkle the cinnamon-sugar mixture evenly over the buttered surface.

Starting from one of the long edges, tightly roll the dough into a log. Pinch the seam firmly to seal it. Gently tuck in the ends to create a neat loaf shape.

Lightly grease a 9x5 inch loaf pan. Carefully transfer the rolled dough seam-side down into the prepared loaf pan.

Cover the loaf pan loosely with plastic wrap or a damp towel and let it rise in a warm place for another 30-45 minutes, or until it has noticeably puffed up and almost reaches the top of the pan.

Preheat your oven to 375°F (190°C) during the last 15 minutes of the second rise.

Bake for 30-35 minutes, or until the top is golden brown and the internal temperature reaches 200-205°F (93-96°C) with an instant-read thermometer. If the top starts to brown too quickly, you can loosely tent it with aluminum foil.

Remove the bread from the oven and let it cool in the pan for 10-15 minutes before carefully transferring it to a wire rack to cool completely.

While the bread cools, prepare the glaze: In a small bowl, whisk together the powdered sugar, 2 tablespoons of milk, and vanilla extract until smooth. If the glaze is too thick, add more milk, 1 teaspoon at a time, until it reaches a drizzly consistency.

Once the bread is fully cooled, drizzle the vanilla glaze generously over the top. Slice and serve.