Preheat oven to 350 degrees. Line a 10" springform pan with parchment paper and grease well with non-stick cooking spray. Set aside.
In the bowl of your stand mixer fitted with the paddle attachment, mix butter and sugar together unitl combined. Add egg, egg yolk and vanilla, and pudding mix and beat until fully incorporated. Add flour, baking soda and salt, stirring until just combined. Do not over-mix. Add 1 cup sprinkles and stir by hand with a rubber spatula. Pat dough down into prepared baking pan and bake for 20-25 minutes until the edges are slightly golden and the top doesn't look "wet" anymore.
While the cookie cake is baking, prepare frosting. beat softened butter until smooth. Add confectioner's sugar. Beat in vanilla and heavy cream 1 tbs at a time as needed to create a creamy consistency that is pipe-able. Add salt to taste. Beat frosting for 3 minutes.
When cookie cake is done, place pan on a wire rack and immediately remove outer ring of springform pan to prevent the edges from browning any further - release edges with a butter knife if needed. Allow cookie cake to cool completely before piping the edges with frosting. You can also just spread the frosting on top of the entire cake. Top frosting with remaining 2 tbs sprinkles.