Preheat the oven to 350°. Line baking sheets with parchment paper.
Combine the flour, baking soda, baking powder and salt in a medium-size bowl.
Cream the cooled melted butter and sugars together in a large mixing bowl with an electric mixer on medium speed until smooth.
Add the eggs, vanilla extract and peanut butter and beat until smooth.
Stir in the flour mixture until just combined.
Place the bowl in the refrigerator for 10 minutes (or up to 6 hours) to let the dough firm up.
Scoop a heaping tablespoonful of dough and roll it between your palms to form a ball.
Place the balls on the baking sheets, leaving about 3 inches between each cookie.
Make a deep impression in the center of each cookie with the chocolate candy. Press the cookie dough up and around the chocolate kiss so that just a little bit of the chocolate peeks out of the top of the ball. (Balls of dough may be placed next to each other on parchment paper-lined baking sheets, frozen, transferred to zipper-lock plastic freezer bags and stored in the freezer for up to 1 month. Frozen cookies may be placed in the oven directly from the freezer and baked as directed.)
Bake the cookies until they are lightly colored, about 12 minutes (a minute or 2 longer for frozen dough).
Let them stand on the baking sheet for 5 minutes, then carefully slide the entire parchment sheet with the cookies from the pan to a wire rack and let them cool completely.