Beat butter with a mixer at high speed until creamy; add brown sugar, beating well. Add granulated sugar and next 3 ingredients; beat until fluffy. Stir in peanuts.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking soda, and salt in a bowl; stir into peanut butter mixture. Cover dough, and chill 30 minutes.
Preheat oven to 350°.
Shape dough into 1-inch balls; place 2 inches apart on baking sheets coated with cooking spray. Press thumb in center of each ball to make an indentation.
Bake at 350° for 10 to 12 minutes or until lightly browned. Press centers again with thumb while cookies are still warm; fill center of each cookie with about 1/2 teaspoon fruit spread. Cool on pans 2 minutes. Remove from pans, and cool completely on wire racks.