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1. Preheat oven to 375 degrees F. In a large bowl, combine butter and peanut butter. Beat with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt. Beat until combined, scraping side of bowl occasionally. Beat in egg and vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. If necessary, cover and chill about 30 minutes or until dough is easy to handle.
2. Shape dough into 1-1/2-inch balls. Press a peanut butter cup half into each ball and shape dough around peanut butter cup to enclose. Place cookies 2 inches apart on an ungreased cookie sheet.
3. Bake in the preheated oven for 8 to 10 minutes or until edges are firm and bottoms are very lightly browned. Transfer cookies to a wire rack; let cool. If desired, sprinkle cookies with cocoa powder. Makes about 42 cookies.