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.

For mini bundts, fill each cavity 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. For a loaf, spread half the batter in the prepared pan, top with cinnamon swirl, and cover with the remaining batter.

For mini bundts, bake at 350°F for 15-20 minutes. For a loaf, bake at 350°F for 40-50 minutes until a toothpick inserted in the middle comes 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. For the loaf, drizzle the cream cheese mixture on top.

Optionally dust with powdered sugar and enjoy.