Preheat oven to 350 degrees Fahrenheit. Spray the cups of a 24-cup mini muffin pan with nonstick spray or grease well with a little oil.
In a large bowl, stir together the flour, baking powder, and salt.
In a medium bowl, whisk together the peanut butter, egg, and sugar until smooth. Add the milk and vanilla and mix.
Pour the wet ingredients over the dry ingredients. Stir with a whisk just until smooth. Don't overmix as that can lead to tough muffins! No one wants tough muffins.
Bake 8-10 minutes, until the tops spring back when you poke them and a toothpick inserted into the center comes out dry.
Remove from oven and place on a rack to cool for about 5 minutes. Using a butter knife to help pry the muffins out of their cups, gently remove the muffins and place them on a wire rack to cool completely, about 20 minutes.
Cut muffins in half, spread on 1/2 teaspoon of jam on the insides of each bottom half, and then replace the top.
Muffins keep in an airtight container at room temperature for 2-3 days.