Preheat the oven to 350 degrees F. Spray a 12-cup muffin tin with cooking spray.
In a food processor, combine the flour, sugar, baking powder, and salt. Pulse in all of the peanut butter until the mixture resembles coarse crumbs. Add the milk, egg, and butter and pulse until combined.
Distribute half of the batter equally among the muffin cups. Drop a teaspoon of jam into each cup and cover with the remaining batter. Top with the chopped peanuts. Bake until the muffins are light golden, 15 to 20 minutes. Transfer them to a wire rack to cool. Serve warm or allow to cool completely. Spread compound butter ontop. Store in an airtight container. The muffins will keep for 1 to 2 days.
Combine ingredients together and chill until set.