In a large bowl, beat butter and peanut butter together.
Add sugars, and beat until well-combined.
Mix in egg and vanilla until combined.
Add flour, baking powder, baking soda, and salt. Stir until combined.
Stir in chopped nuts.
Cover, and chill dough for 1 hour, or until firm.
Toward the end of the chilling time, preheat oven to 350 F.
Scoop out 1.5 tablespoons of dough and place on prepared cookie sheet 2 inches apart. I've slightly flattened the cookies and left them as-is, and it doesn't seem to make much difference.
Bake 10-15 minutes, or until edges are lightly browned and middles are set.
Let cookies cool on the cookie sheet for 5 minutes.
Remove to wire rack, and let finish cooling.
Top cookies with jelly or spread jelly between two cookies to make a sandwich.