I made
Candy Cane Cookies. It's basically a butter cookie, but I used vanilla extract instead of peppermint, not sure where to find the latter without alcohol in it. I supposed you could crush some candycanes and sprinkle that on top before baking or into the dough to substitute the extract but I don't think I'd be a fan of peppermint cookies anyway. They taste yummy the way I made them though. Next time I'll try to make them thinner but it's hard to twist the dough that thin without it breaking.
before going in the oven:

after:

2.5 cup flour
pinch salt
1 cup soft butter
3/4 cup sugar
1 large egg
1 tspn peppermint extract
1/2 teaspn vanilla extract (I used 1 teas)
1/2 teas (or more) red food coloring
1. combine flour and salt in a little bowl. In another bowl, beat sugar, butter, egg, vanilla.
2. divide dough in half. color one with red color. cover halves separately and chill for 30 minutes.
3. preheat oven to 350. take 1 teas of red dough and 1 teas of white and roll into 6 inch long ropes. place them side by side and twist. Curve an end.
4. bake 8-10 min til bottom is lightly golden.