Preheat oven to 350°F (175°C).
Prepare birthday crumbs: Combine 100g sugar, 25g brown sugar, 90g cake flour, 2g baking powder, 2g salt, and 20g sprinkles. Add 40g oil and 4g clear vanilla; mix until clusters form. Bake for 15 minutes.
Prepare cake: Cream 115g butter and 250g sugar. Add 3 eggs and beat for 3 minutes. Stream in buttermilk, 40g oil, and 8g clear vanilla. Fold in 185g cake flour, 4g baking powder, 2g salt, and 30g sprinkles. Spread on a lined quarter-sheet pan and bake for 30 minutes.
Prepare frosting: Cream 115g butter, 60g shortening, and 55g cream cheese with glucose and corn syrup. Add powdered sugar, salt, a pinch of baking powder, and citric acid. Whip until pale white.
Assemble: Cut two 6-inch rounds and cake scraps from the sheet. Place a 6-inch cake ring on a tray lined with acetate. Layer cake scraps at bottom, brush with milk soak (milk + vanilla), spread frosting, and top with crumbs. Repeat with cake rounds. Freeze for 6 hours before removing ring.