Whisk flour, baking soda, baking powder, and salt together. Set aside.
Cream butter and sugar until light and fluffy. Beat in eggs one at a time, then add vanilla and sour cream.
Gradually add dry ingredients until combined. The dough will be sticky.
Shape dough into a disc, wrap in plastic, and refrigerate for at least 2 hours.
Prepare browned butter for filling and let cool. Mix with brown sugar and cinnamon.
Divide chilled dough into thirds. Roll each into a rectangle about 13 × 7 inches.
Spread each with browned butter mixture, patting filling gently into dough.
Roll tightly into logs, wrap in parchment, and freeze for 30 minutes.
Preheat oven to 350°F. Line baking sheets with parchment.
Slice logs into ¾-inch cookies. Place on prepared sheets 1 inch apart.
Bake 9–11 minutes until set but not browned. Cool briefly, then transfer to a rack.
For the glaze, whisk browned butter and cream cheese until smooth.
Add powdered sugar, vanilla, and milk to desired consistency.
Drizzle over cookies and let set.