In a large mixing bowl, combine the sourdough discard, milk, sugar, melted butter, and egg. Mix until combined.

In a separate bowl, whisk together flour, salt, and instant yeast. Gradually add the dry mixture to the wet mixture, stirring until a soft dough forms.

On a lightly floured surface, knead the dough for about 5-7 minutes until smooth and elastic.

Place the dough in an oiled bowl, cover it with a clean towel or plastic wrap, and let it rise in a warm spot for 1 hour, or until doubled in size.

While the dough rises, combine cinnamon and brown sugar in a bowl. Set aside.

Once the dough has risen, punch it down and roll it out on a floured surface into a rectangle (about 1/4-inch thick). Spread the softened butter on top, then sprinkle evenly with the cinnamon-sugar mix.

Starting from the long side, carefully roll the dough into a tight log. Pinch the seams to seal and cut the log into 12 equal pieces.

Arrange the rolls in a greased baking pan. Cover and let rise for another 30-45 minutes.

While the rolls are rising, preheat your oven to 375°F (190°C).

Bake the rolls for 20-25 minutes, or until golden brown.

While the rolls are baking, whisk together powdered sugar, milk, and vanilla (if using) until smooth.

Once the rolls are out of the oven, let them cool slightly before drizzling with the glaze.