Preheat your oven to 375 degrees Fahrenheit and grease a 9-inch by 13-inch rectangular baking pan with butter.
In a large bowl using a hand mixer or in the bowl of your stand mixer, beat the butter and sugar on high speed for several minutes until they're creamed together (fluffy and smooth and pale in colour).
Beat in the sour cream, egg, and vanilla extract until well incorporated.
Add the flour, baking powder and salt and mix on low speed just until combined. The mixture may appear slightly crumbly but this is totally normal.
Press the mixture into the bottom of the prepared baking pan with your hands or a flat kitchen object like the bottom of a measuring cup.
Bake the sugar cookie base at 375 degrees Fahrenheit for about 16-17 minutes, making sure that no browning occurs on the edges. If the edges start to brown, remove the base from the oven immediately.
Let the sugar cookie base cool completely to room temperature while you make the frosting.
In a large bowl using a hand mixer, or in the bowl of your stand mixer, whip the butter on high speed until it's ultra smooth and pale in colour.
Add the powdered sugar 1/2 cup at a time until it's well incorporated.
While the mixer is running, add the whipping cream in a steady stream until the desired consistency is reached (spreadable, but not too thin). You may only need to add 4 or 5 tablespoons of whipping cream.
Add the vanilla and sea salt and food colouring and whip on high speed until the frosting becomes light and fluffy (about 4-5 minutes).
Spread the frosting over the completely cooled sugar cookie base and top with sprinkles.
Refrigerate for about 30 minutes before slicing to allow the icing to set (this will create clean slices).