Whisk together flour, cocoa, and salt in a bowl. Beat butter and sugar with a mixer until combined. Beat in egg, then vanilla and beat for 1 minute. Reduce speed to low and gradually beat in flour mixture until combined. Shape dough into a disk, and wrap in plastic. Refrigerate until firm, at least 2 hours.
Roll out dough to 1/8" thick. Transfer to a baking sheet and refrigerate until firm.
Preheat oven to 325 F. Cut out heart shapes using cookie cutters. Cut a smaller heart from the center of each cookie using cookie cutters that are about 1" smaller than the larger cutter used. Transfer the cookies to parchment-lined baking sheets, spacing each 1" apart. Bake until slightly firm, about 12 - 15 min.
Fill the center of each cookie with ground peppermints. Bake until cookie melts, about 6 minutes. Let cookies cool on sheets set on wire racks for 10 minutes. Transfer cookies to racks, and let cool completely.
It would have been a perfect recipe if I had been able to find my set of heart cookie cutters. I used to have about seven different heart shaped cookie cutters, each one just a bit bigger than the other. My girls love them. They're excellent for playing with play dough and for pretending in the little mini-kitchen and for just carting around. I made this cookie dough early in the week and have spent the past few days rummaging through all the toy baskets and boxes in a failed attempt to find the largest heart shape. With the dough in the fridge and the candies on my counter, I could not just abort the recipe. I could use circles, but hey, it's almost Valentine's Day. I'm determined to find a large heart shaped cookie cutter, no matter what I have to do.