Preheat your oven to 350°F. In a large bowl, beat the unsalted butter until smooth. Add the peanut butter and both granulated and brown sugars. Beat until the mixture is light and creamy.
Beat in the egg and vanilla extract until well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually blend the dry ingredients into the wet mixture until just combined.
Using a small scoop or tablespoon, roll the dough into 1 1/2 tablespoon-sized balls. Roll each ball in additional granulated sugar and place them about 2 inches apart on a baking sheet lined with parchment paper.
Gently press your thumb into the center of each ball to create an indentation and spoon about 1 teaspoon of raspberry jam into each.
Bake for 8 to 10 minutes, or until the edges are set. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.