Momofuku's Birthday Cake turned into more manageable and still crazy yummy Birthday Cupcakes.
Preheat oven to 350°. Prepare 2 muffin tins, each with 12 cups, with non-stick muffin cups or butter.
Whisk flour, baking powder, salt, and 1/4 cup sprinkles in a large bowl. Combine buttermilk, oil, and vanilla in a medium bowl.
Using an electric mixer on medium-high, beat granulated sugar, shortening, butter, and light brown sugar in another large bowl until light and fluffy, about 4 min. Add eggs one at a time, beating to blend between additions and occasionally scraping down sides and bottom of bowl. Continue to beat mixture, occasionally scraping down sides and bottom of bowl, until almost doubled in volume and very light, airy, and pale yellow, about 4 min.
With mixer on low, add buttermilk mixture until incorporated. Add dry ingredients, beating until just combined, about 1 min.
Distribute evenly into prepared muffin tins. I found this easiest to do with a small ice cream scoop. I suspect a 1/4 cup measuring device would produce equal results.
Bake for 20-25 minutes until tops are golden brown and a cake tester (toothpick, butter knife, etc.) come out of muffins cleanly. Let cool in tins for 5 min and then cool completely on a wire rack (or in the fridge if you're pressed for time and want to ice the muffins shortly after baking).
Combine butter, shortening, and cream cheese in large bowl of a stand mixer fitted with the paddle attachment (or the flat beater attachment if you don't have the paddle attachment like me). Beat on medium-high until mixture is smooth and fluffy, 2–3 minutes. Scrape down sides of bowl and slowly stream in corn syrup and 1 tbsp vanilla. Beat until mixture is silky smooth and glossy, about 3 min.
Scrape down sides of bowl and, with mixer on low, add powdered sugar, salt, baking powder, and lemon juice until just combined. Increase speed to medium-high and beat until you have a brilliant stark white (or off-white), beautifully smooth frosting, about 4 min (it should look just like it came out of a plastic tub at the grocery store!).
Pipe icing onto muffins and top with sprinkles.