Preheat the oven to 350°F (175°C). Grease a mini bundt cake pan with butter, then dust with flour.

Add the butter to a saucepan over medium-high heat. Allow to melt and slightly brown, stirring continuously for approximately 5-8 minutes. Remove from heat and let it cool for 5-10 minutes.

Sift the flour, baking powder, baking soda, and salt together in a medium bowl. Set aside.

Combine the cooled brown butter with the granulated sugar and brown sugar in a large bowl. Whisk to combine. Beat in the eggs one at a time until incorporated. Add the sourdough discard, Greek yogurt, and vanilla, whisking until smooth. Gently fold in the dry ingredient mixture until just combined. Avoid overmixing.

In a small bowl, mix the brown sugar and cinnamon together.

Fill each cavity of the mini bundt pans approximately 1/3 full with cake batter. Sprinkle around 1 tbsp of cinnamon swirl mixture over the batter. Fill the remaining 2/3 with batter to reach 3/4 full in total, smoothing the tops.

Bake at 350°F for 15-20 minutes. Check for doneness by inserting a toothpick in the middle; it should come out clean.

While the cakes bake, beat together the cream cheese, powdered sugar, and milk in a medium bowl until smooth.

Allow the baked cakes to cool for 10 minutes before inverting onto a wire rack. Once cooled, fill the center of mini bundts with the cream cheese filling. Optionally drizzle the cream cheese mixture on top.

Dust with powdered sugar and enjoy.