Preheat oven to 350°F (180°C). Spray a 9-inch round cake pan with baking spray with flour.
Assemble the Ankarsrum with the stainless steel bowl. Place the dough knife in the smaller hole, and position the dough roller just off the side of the bowl. Beat butter by slowly increasing mixer speed to medium-high (6 o’clock) until creamy, about 1 minute, using the scraper to help move butter around. (Butter might stick to the roller in the beginning.) Slowly add sugars, scraping bowl frequently. Let mix until well combined and lightened in color, about 3 minutes. Add egg and egg yolk, beating until just combined. Beat in vanilla.
In a medium bowl, whisk together flour, baking powder, and salt. With mixer on the lowest speed (12 o’clock), gradually add flour mixture to butter mixture. Move roller to 1 inch away from side of bowl, and increase mixer speed to medium-low (2 o’clock), mixing until combined. Gently fold in ½ cup (80 grams) sprinkles by hand. Press batter into prepared pan. Sprinkle top with remaining 1 tablespoon (10 grams) sprinkles.
Bake until center is set and a wooden pick inserted in center comes out clean, about 30 minutes. Let cool completely in pan. Remove from pan.
Place half of Vanilla Buttercream in a pastry bag fitted with a round piping tip (Ateco #805). Place remaining buttercream in a pastry bag fitted with a small open star piping tip (Ateco #822). Alternate piping rounds and stars around edge of cookie. Garnish with sprinkles, if desired.