Preheat the oven to 375 degrees F. Prepare a 9- by 13-inch baking dish by coating it with butter.
Combine the butter, brown sugar and granulated sugar in a large bowl. Beat with an electric mixer until light and fluffy, 3 to 4 minutes.
Scrape down the sides of the bowl and beat in the extracts. Add the eggs, one at a time, beating well after each addition. Add the milk and beat again until smooth.
In a separate bowl, whisk together the flour, baking soda and salt. Add half of the flour mixture to the wet ingredients and gently mix to incorporate. Add the remaining flour and mix again. Stir in the rainbow sprinkles and any additional mix-ins you choose.
Spread the batter into an even layer in the prepared pan. Bake until just set in the center, 20 to 25 minutes. Cool on a rack before slicing and decorating as desired.