Cream the butter and powdered sugar together until smooth and fully combined, scraping down the bowl as needed. Mix in the vanilla extract.
Add the flour and salt and mix on low speed just until the dough looks crumbly and starts to clump. At this point, stop the mixer.
Use your hands to gently press and knead the dough together in the bowl. If the dough will not come together when pressed, add milk or cream 1 teaspoon at a time, kneading gently after each addition, just until a smooth dough forms. The dough should hold together easily without feeling sticky.
Divide the dough evenly in half. Knead red gel food coloring into one half until evenly colored. If the colored dough feels slightly softer than the plain dough, that’s normal.
Place each dough between two sheets of parchment paper and roll into rectangles about ¼ inch thick, keeping them roughly the same size.
Peel off the top parchment, stack the doughs on top of each other, then gently roll into a tight log, starting from the long edge. Wrap the log tightly in parchment or plastic wrap.
Chill the dough for at least 1 hour, or until firm enough to slice cleanly.
Preheat the oven to 325°F and line a baking sheet with parchment paper.
Slice the chilled dough into ¼-inch rounds and place them on the baking sheet about 1½ inches apart.
Bake for 12–15 minutes, just until the cookies are set. Do not let them brown.
Cool on the baking sheet for 5 minutes, then transfer to a rack to cool completely before stacking or packaging.