In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugar until well blended, 1 to 2 minutes. Add vanilla extract and salt. With mixer on low speed, gradually add flour, scraping down sides of bowl.

Turn dough out onto a clean work surface; it will be loose and crumbly. Knead dough until it begins to hold together, about 1 to 2 minutes. Divide dough in half. Add the food coloring to one of the halves and knead until fully incorporated.

Divide each dough into 2, to make 4 balls of dough (2 of each color). Using your hands and a ruler, roll out one dough ball into a 11 inch rope and flatten each side with a bench scraper to make a long square shape. Repeat with remaining 3 balls of dough and alternate and stack to make a 4 square checkered dough, press gently to adhere them together. Wrap in plastic wrap and refrigerate 30 minutes, or freeze 15 minutes.

Preheat oven to 350 degrees. Line a baking sheet with a parchment paper. Slice each log into 1/4-inch-thick slices; place on baking sheet. Bake until done, 10 to 12 minutes. Remove baking sheet from oven, and let cookies cool 2 minutes. Transfer cookies to a wire rack to cool completely.