In a small bowl, whisk together the flour, baking soda and salt then set aside.
Beat together the butter, peanut butter and both sugars on medium speed until light and fluffy. Add the egg and vanilla and mix for another minute or so to combine. Reduce the mixer speed to low, add the dry ingredients, and mix until just combined.
Shape the dough into 1-inch balls (about 2 teaspoons worth of dough) and place in the cups of a miniature muffin pan (keep the dough in balls – do not press into the pan).
Bake for 8 to 10 minutes, or until light golden brown and slightly puffy. Remove from the oven and immediately press a miniature peanut butter cup in the middle of each cookie, pressing down so that the top of the peanut butter cup is even with the top of the cookie. Cool for at least 10 minutes before removing from the pans, and let cool completely. Store in an airtight container at room temperature.