Butter a 13 by 9-inch baking dish and line with parchment paper with a 1-inch over hang on all sides. Set aside.
In the bowl of an electric stand mixer (you can also use a hand mixer too), cream together butter and sugar until well combined. Add vanilla extract and salt and mix together. Slowly add flour with mixer set on low and mix until combined. The mixture will start out dry and pebbly but will come together, although it won't be creamy like most cookie dough. Gently fold in 2 1/2 Tablespoons of sprinkles.
Press dough into an even layer in prepared pan. Sprinkle with another 1/2 Tablespoon of sprinkles, gently press into dough. Chill for 20-30 minutes in the refrigerator.
Preheat oven to 350 degrees. Using parchment overhand, lift dough from pan. Cut 1/2 squares with a sharp knife (make rows, don't try to individually cut 1/2 pieces).
Transfer about 1/3 of the cookies to an unbuttered cookie sheet, spacing cookies 1/2-inch apart. Put remaining cookie batter in the refrigerator.
Bake for 8-12 minutes. Remove to another baking sheet to cool. Repeat process with remaining cookies. Store cookies in an airtight container at room temperature.