Heat oven to 350°F and line a 12-cup muffin pan with paper liners.
Whisk flour, baking powder, and salt in a medium bowl.
Beat butter, peanut butter, granulated sugar, and brown sugar until light and fluffy.
Mix in eggs one at a time, then beat in the vanilla.
Add dry ingredients in three additions, alternating with milk. Mix just until smooth.
Divide batter among liners, filling each about two-thirds full.
Bake 17 to 19 minutes, until a toothpick comes out clean. Cool completely.
Core each cupcake with a small knife. Spoon jam into the centers and replace the tops.
Beat butter and peanut butter for frosting until creamy and well combined.
Gradually beat in powdered sugar and salt. Add milk until light and spreadable.
Pipe or spread frosting onto cupcakes. Swirl extra jam and sprinkle peanuts, if using.
Serve right away or store airtight at room temperature up to 1 day, or refrigerate 3 days.