Preheat oven to 350 degrees F. Have ready a greased mini muffin pan or an ungreased silicone muffin pan.
Beat the butter and both sugars together. Beat in the peanut butter and egg, then scrape sides of bowl and beat in the salt, baking soda and vanilla. Add flour and stir until blended.
Shape dough into 1-inch balls or scoop with a small cookie scoop. Set the balls into the muffin pans. No need to press. These should spread on their own.
Bake for 10 to 12 minutes at 350F, then pull from oven and press a mini peanut butter cup into the center of each. Return to the oven for 1-2 minutes to soften chocolate.
Allow the cookies to cool in the cups for about 20 minutes, the carefully loosen and let cool on a wire rack.
Notes
**If you only have salted butter you can use that, but reduce the salt in the recipe to about ¼ teaspoon.