The sourdough discard brioche dough can be mixed by hand or in a stand mixer.
Warm the milk in the microwave for 30-45 seconds and pour it in a mixing bowl.
Stir in the sourdough discard and sugar until mostly dissolved. Then whisk in the egg and vanilla extract.
To a separate bowl whisk together the flour, baking soda, baking powder, & salt, and slowly add it to the wet mixture along with the softened butter.
Mix until the ingredients come together into a shaggy dough, then cover and let it rest for 20–30 minutes to hydrate and relax.
After resting, knead the dough until it becomes fairly smooth, being careful not to add too much extra flour, as this can alter the final texture. It should remain slightly sticky even after kneading.
Once complete, cover the dough and let it rest for another 15-30 minutes.
Line a 12 cup muffin pan with muffin liners and preheat the oven to 350 degrees F.
In a bowl, combine the brown sugar, granulated sugar, and cinnamon, then whisk until evenly mixed.
After resting, roll the dough out on a lightly floured surface into a 20x10-inch rectangle.
Spread the softened butter evenly over the dough, leaving a ½-inch border. Sprinkle the cinnamon-sugar mixture over the top, then gently press it into the dough to help it adhere.
Using a ruler or visually estimating, lightly score the top of the dough every 1.5 inches to help guide the cuts and maintain uniformity. Use a pizza cutter to make clean, straight cuts through the dough. You will end up with 12 muffins.
Individually roll each cinnamon roll and place them into the muffin pan.
Bake the sourdough discard cinnamon roll muffins for 23-25 minutes or until the internal temperature is 190-200 degrees F.
Allow the muffins to rest for 10-15 minutes before removing from the pan.
While they rest, make the cream cheese frosting.
Using your electric hand mixer, beat the cream cheese and butter together on medium speed in a medium mixing bowl. Mix until they are well combined and have a smooth, creamy texture.
Pour the vanilla extract in and mix until combined.
Reduce the speed of your hand mixer to low. Slowly add the powdered sugar, about one cup at a time.
After each addition of powdered sugar, increase the mixer speed to medium and continue to blend until the frosting becomes smooth and well combined.
Top each sourdough cinnamon roll muffin with the cream cheese frosting and enjoy!
