Preheat oven to 400ºF and spray a muffin pan with nonstick cooking spray. In a medium bowl, whisk the flour, baking powder, baking soda, and salt together; set aside.
In a stand-mixer fitted with a paddle attachment, cream the butter and both sugars together on medium-high until light and fluffy--about 3 minutes. Add eggs, one at a time, mixing well after each addition. Add vanilla.
Mix in a third of the flour mixture, followed by a third of the sour cream. Continue to alternate between the dry mixture and sour cream, until everything has been incorporated. Batter will be VERY thick.
Scoop about 2 Tablespoons of the batter into each muffin well, using two forks to spread batter into the bottom and up the sides of the muffin well.
Spoon about 1 Tablespoon of peanut butter into the center of the muffin batter and top with about a teaspoon of the jam. Top with about 1-2 Tablespoons of batter, ensuring the peanut butter and jam are completely covered.