Preheat oven to 375°F (190°C). Line a 12-cup muffin tin with liners.
In a small saucepan, melt butter over medium heat and cook until golden brown and fragrant. Let cool slightly.
In a large bowl, whisk together milk, sour cream, eggs, vanilla, and both sugars. Whisk in the browned butter.
In another bowl, mix flour, baking powder, baking soda, and salt.
Add dry ingredients to the wet mixture and stir until just combined.
Gently fold in blueberries.
Divide batter evenly among muffin cups. Bake 20-22 minutes, until tops are golden and a toothpick comes out clean.
Let muffins cool 10 minutes.
For the glaze, whisk powdered sugar, lemon juice, and zest until smooth. Drizzle over warm muffins.