Prepare streusel: In a medium bowl, stir together brown sugar, flour, cinnamon, and salt. With a pastry blender or two knives, cut in butter until mixture resembles large coarse crumbs; refrigerate until ready to use.
Prepare muffins: Preheat oven to 350 degrees. Butter and flour two jumbo 6-cup muffin pans. In a small bowl, whisk together flour, baking powder, and baking soda; set aside.
Using an electric mixer, beat together butter, sour cream, granulated sugar, and vanilla on medium speed until light and fluffy. Beat in eggs, one at a time, until well combined. With mixer on low, beat in flour mixture just until combined.
Divide half the batter among muffin cups; top with half the streusel. Cover with remaining batter; top with remaining streusel. Bake until a toothpick inserted in the center of a muffin comes out clean, 25 to 30 minutes. Cool in pan 5 minutes, then transfer to a rack to cool completely. Dust with confectioners' sugar before serving.