Preheat oven to 350°F. Butter one 12x18-inch sheet pan, two 9x12-inch sheet pans or 24 cupcake tins.

In the bowl of an electric mixer, beat butter until pale and creamy. Beat in the sugar. Beat in the 3 egg whites one at a time, then the whole egg. Stir in vanilla and vegetable oil.

In a medium bowl, stir together flour, baking powder and salt. Add flour mixture to the egg mixture 1/2 cup at a time, beating well in between. As needed, scrape down the sides of the bowl with a spatula. Beat in the milk. On low speed or by hand, fold in the sprinkles/jimmies.

Bake for 20-25 minutes or until sides are slightly browned and a cake tester comes out clean. Allow to cool completely on wire racks

With an electric mixer, beat butter on medium speed for 2 minutes, until pale and creamy. Add the confectioners' sugar 1/2 cup at a time. Beat on medium speed until well-beaten, scraping down the sides of the bowl with a spatula as needed. After each addition, beat the mixture on high speed for 10 seconds to aerate the frosting.

Beat in vanilla until frosting is smooth. Store in an airtight container and refrigerate for up to 10 days. Bring to room temperature before using.

Meanwhile, prepare the push-pop containers. Cut the cake into circles. Cut the sheet cakes with a circular biscuit cutter small enough to just fit into the push-pop containers. With the biscuit cutter, cut the cake or cupcakes into small pieces. (Cupcakes may need to be sliced horizontally as well.)

Prepare a piping bag with a star nozzle and fill with frosting. To make a push pop, place one cake circle in the base of the push-pop containers. Working in a circular motion, top the cake circle with a swirl of frosting. Top with a pinch of nonpareil sprinkles. Add another cake circle, frosting and more sprinkles. Repeat once more (three layers total) and top with more sprinkles. Serve or cover with lids if not enjoying right away.