Heat Treat the Flour: Preheat the oven to 300ºF (149ºC) and add the flour on top, smoothing it down into a fairly even layer. Bake in 2 minute increments until the temperature of the flour reaches 160ºF (71ºC). You can check by inserting a food grade thermometer into the deepest pile of the flour. It took about 4 minutes for mine to reach 160ºF (71ºC).
Once the flour reaches this point, remove it from the oven. Carefully lift up the parchment paper and use it to slide the flour into a separate bowl. Set aside to cool for 20-30 minutes, until the flour is room temperature, before moving on to the next step.
In the bowl of a stand mixer fitted with the paddle attachment (or with a large bowl and hand mixer), add the butter, granulated sugar, and powdered sugar. Beat on high speed until light and creamy, about 2 minutes.
Add the heavy whipping cream, vanilla extract, almond extract, and salt. Mix on medium speed until fully combined, 1-2 minutes. Add the heat treated (now room temperature) flour and continue mixing on low speed until the mixture forms a uniform dough, about 1 minute, then fold in the sprinkles.
Form the Cookie Dough Discs: Using the same diameter cake pans you used to bake the vanilla cake, line the bottoms with wax or parchment paper. If you baked three 6-inch cake layers, divide the cookie dough into two equal portions and line the bottom of two 6-inch cake pans. Press the dough into each cake pan until it is about 1/4 inch thick disc, leaving about 1/2 inch between the edge of the disc and the edge of the cake pan. If you baked two 8-inch layers, line the bottom of one 8-inch cake pan and press all of the dough into one disc, leaving the same 1/2 inch space between the disc and cake pan edge.
Refrigerate the cookie dough disc(s) for about 15 minutes to make them easier to handle before using them in the cake assembly. Alternatively, you can wrap the whole disc in plastic wrap and refrigerate the dough up to one week ahead.