Heat the oven to 350°F (177°C) and grease a 9-inch springform pan. Coat the pan evenly so the baked cake releases without tearing.

Whisk the flour, baking powder, baking soda, and salt in a medium bowl, then set it aside. The dry mixture should look evenly blended with no visible pockets of leavening.

Beat the softened butter and sugar for about 3 minutes until pale and creamy, then beat in the egg and vanilla on high speed. Scrape the bowl as needed so no buttery streaks remain around the sides.

Mix in the dry ingredients and milk on low speed until combined, then scrape the bottom with a spatula and spread the thick batter in the pan. The batter should be even and free of large lumps before it goes into the oven.

Bake for 30-36 minutes, tenting loosely with foil if the top darkens too quickly. A toothpick inserted at the center should come out clean when the cake is done.

Cool the cake completely in its pan on a wire rack. The cake must feel fully cool before it is crumbled so the frosting does not melt into it.

Beat the frosting butter on medium speed for about 2 minutes, then mix in the confectioners sugar, cream, and vanilla on low. Increase to high speed and beat for 3 minutes until the frosting is smooth and creamy.

Break the cooled cake over the frosting, removing any very crisp edges if they seem tough, then mix on low until combined. The crumbs should become a uniform, moldable mixture with no large cake pieces.

Scoop 1 Tablespoon (about 20g) of mixture and roll it into a ball on a lined baking sheet. Each ball should be about 1 inch wide and smooth enough to hold its shape.

Refrigerate the balls for 2 hours, or freeze for 1 hour, then reroll any that have flattened and return the tray to the refrigerator. Work with only a couple of cold balls at once so they remain firm for dipping.

Melt the candy melts or chocolate in a 2-cup liquid measuring cup, microwaving in 20-second intervals and stirring after each round. Stop when the coating is glossy and fluid, with no unmelted lumps.

Take out 2 or 3 chilled cake balls, dip about 1/2 inch of each lollipop stick in coating, and push it halfway into the center. You should feel slight resistance as the stick settles into the cold ball.

Lower each pop straight into the coating until covered, including the joint where the stick meets the cake ball. A single vertical dip keeps the surface smooth, so avoid swirling the pop in the cup.

Tap your wrist gently against the measuring-cup rim to release excess coating, then add sprinkles and stand the pop upright in a styrofoam block or box. The coating should drip in a thin ribbon rather than collect in a heavy puddle at the bottom.

Let the coating set for up to 1 hour before storing the finished pops in the refrigerator. The shell is ready when it feels firm and dry to the touch.