Preheat your oven to 325°F (165°C) fan-assisted. Line 2 baking sheets with parchment paper and set aside.
In a small bowl, combine the flour, baking soda, baking powder, and salt together until well mixed. Set aside.
Using a hand whisk or stand mixer, cream the butter and peanut butter together until smooth, about 1 minute.
Mix in the granulated sugar and dark brown sugar, and beat until light and fluffy, about 2 minutes.
Add the egg, whole milk, and vanilla extract. Mix until well combined.
Gradually stir in the dry ingredients, then fold in the chopped peanuts.
Scoop out a heaped tablespoon of dough, roll into a smooth ball, and flatten it into a 2-inch (5 cm) disc. Place the discs about 3 inches (7 ½ cm) apart on the prepared baking sheets.
Press your thumb into the center of each disc of dough to create a small divot.
Spoon ½ teaspoon of seedless raspberry jam into each divot.
Bake the cookies for 20-22 minutes, or until set and the edges begin to brown.
While the cookies are still hot, add an additional ½ teaspoon of jam into the center of each cookie. Let cool completely.
Store in an airtight container at room temperature for up to 2 days. If stacking, place parchment paper between layers.