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 and mini chips, if using.
Cover, and chill dough for 1 hour, or until firm. Don't skip this step, or the cookies will bake out.
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.
Notes
Can use regular-sized, jumbo, or mini chocolate chips or chunks.