Preheat the oven to 350°F. Generously grease each cavity of a mini bundt pan with butter or non stick spray, then lightly dust with flour. Tap out any excess so the cakes release easily after baking.

Brown the butter in a medium saucepan over medium heat, stirring constantly for 5 to 8 minutes. It will foam, then turn golden with brown specks and a nutty aroma. Remove from heat right away and let cool for 5 to 10 minutes. If it smells burnt, discard and start again.

In a medium bowl, sift together the flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, whisk the cooled brown butter with granulated sugar and brown sugar until smooth. Add the eggs one at a time, mixing well after each addition. Stir in the Greek yogurt, sourdough discard, and vanilla until fully combined.

Gently fold the dry ingredients into the wet mixture just until no dry streaks remain. Do not overmix. If the batter seems very thick, let it rest for about 2 minutes.

In a small bowl, mix the brown sugar and cinnamon until evenly combined.

Fill each bundt cavity about one third full with batter. Sprinkle roughly 1 tablespoon of the cinnamon sugar over the batter, then top with more batter until nearly full, smoothing the surface gently.

Bake for 15 to 20 minutes, until the tops are lightly golden and spring back when touched. A toothpick inserted in the center should come out clean.

While the cakes bake, beat the cream cheese, powdered sugar, and milk until smooth and creamy. Start with 3 tablespoons of milk and add more as needed for a thick, pipeable consistency.

Let the cakes cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely. Use a small knife or piping bag to create a center opening and fill with the cream cheese mixture.