How to Make It
Preheat oven to 375°. Place brown sugar, granulated sugar, and butter in a large bowl; beat with a mixer at medium speed until well blended (about 3 minutes). Add egg, beating well. Beat in 1/2 cup sour cream and vanilla. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, salt, stirring well with a whisk. Add flour mixture to sugar mixture and sprinkle in blueberries; beat at low speed just until combined.
Spoon batter into a large zip-top plastic bag. Snip a hole in the bottom corner of bag; pipe batter evenly into 10 doughnut cups coated with baking spray, filling about two-thirds full. Bake at 375° for 14 to 15 minutes or until a wooden pick inserted in center comes out clean. Cool on a wire rack.
Combine powdered sugar and remaining 1 tablespoon sour cream in a small bowl, stirring with a whisk until smooth. Divide glaze in two bowls. By the drop, add 2 drops of red food coloring to the glaze. Take a toothpick and make a few colored swirls in the glaze, but do not overmix. Using a spoon, drizzle glaze into "stripes" over doughnuts. The streaks of color will create a "tie-dye" effect. Repeat process with blue, designating the top left corner as the stars on an American flag. Let glaze set and serve.