Preheat the oven to 375°F and line a 12-cup muffin tin with paper liners.
Melt the butter in a small saucepan over medium heat, swirling often, for 4-6 minutes until it foams and turns golden brown with toasted bits and a nutty aroma. Pour into a bowl, scraping in all the brown bits, and cool for 10 minutes.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, cardamom, cloves, allspice and pepper.
Blend the cottage cheese, eggs, brown sugar, milk and vanilla until smooth. Add the brown butter and pulse 2-3 times to combine.
Pour the wet mixture into the dry ingredients and fold just until combined.
Divide the batter among the cups and bake for 18-22 minutes, until domed and a toothpick comes out clean. Cool completely on a wire rack.
Whisk the powdered sugar, maple syrup, milk and cinnamon into a thick but pourable glaze. Dip the top of each muffin into the glaze and let it set for 10 minutes.