Make the Base Sugar Cookie Dough: Whisk the flour, baking powder, and salt in a bowl.
Beat the butter and sugar in a stand mixer fitted with the paddle attachment until fluffy and creamy, stopping the mixer and scraping down the sides midway if you have to, 3–4 minutes. Stop the mixer, then add the eggs and vanilla, return to medium speed and beat until creamy, 2 minutes. Stop the mixer, add the dry ingredients, then turn on the mixer to low and beat until everything is incorporated, being careful not to overwork the dough. Divide the dough into three equal-sized pieces.
Make the Peanut Butter & Jelly Cookies: Before chilling, add 2 tablespoons creamy peanut butter to one third of the dough (you can do this in the stand mixer or by hand). Wrap the dough in plastic wrap and chill for 1 hour.
Remove the dough from the fridge, unwrap, and divide the dough into 20 equal-sized pieces (about a tablespoon of dough each). Roll each piece into a ball, then roll in ½ cup finely chopped salted peanuts, pressing to adhere. Arrange three inches apart on parchment-lined baking sheets and press a ½-inch-wide hole into the ball with your thumb, smoothing it out to make that divot into as much of a perfect circle as possible. Fill each hole with ½ teaspoon raspberry or strawberry jam.
Chill for 1 ½ hours, preheating the oven to 325°F in the last 15 minutes of chilling. Bake until lightly golden around the edges, 12–13 minutes. Cool completely. Store in an airtight container for up to four days.