Preheat oven to 350F degrees. Prepare a large baking sheet by lining it with parchment paper.
Chop the peanuts using a sharp knife into small pieces. Set aside.
In a medium-sized bowl, combine the flour, baking soda, baking powder, and salt, whisk (or use a fork) to combine.
In a large mixing bowl, combine the cooled melted butter with the brown sugar and white sugars and mix on medium speed with an electric hand mixer until smooth. Add in the eggs, vanilla and peanut butter mixture and beat until smooth, 1-2 minutes. Next, add the flour mixture into the butter/sugar mixture in two steps - mixing just until combined. Stir in the chopped peanuts.
Refrigerate the dough in the bowl for at least 30 minutes to firm up before baking. The dough can be made and refrigerated for up to 3 days before baking.
Scoop a heaping tablespoon of cookie dough (about 1 ½ tablespoons) and roll it into a ball with your hands. Place it on the prepared cookie sheet placing each cookie at least three inches apart from each other.
Bake the cookies until very lightly colored around the edges, about 15 minutes.
Remove from oven and while the cookies are warm, use the back of a spoon to gently make a small indentation in the middle of each cookie. This is where the jam will go later.
Cool the cookies completely, then add a teaspoon of jam into each indentation and serve.