Preheat the oven to 350°F, rack in the middle position.
Microwave the butter in a microwave safe mixing bowl for approximately 90 seconds on HIGH to melt it.
Mix in the brown sugar, white sugar, vanilla, baking soda, baking powder, and salt. Stir until they're thoroughly blended.
Measure out the peanut butter.
Add it to the bowl and mix it in.
Pour in the beaten eggs and stir it all up. Add the chopped salted peanuts and mix until they're incorporated.
Add the flour in one-cup increments, mixing it in until all the ingredients are thoroughly blended.
Form the dough into walnut-sized balls with your hands and arrange them on a greased cookie sheet, 12 to a standard sheet. (If the dough is too sticky to form into balls, chill it for an hour or so, and then try again.)
Make an indentation in the center of the dough ball with your thumb. Spoon in a bit of jam, making sure it doesn't run over the sides of the cookie.
Bake at 350°F for 10 to 12 minutes, or until the tops are just beginning to turn golden. Cool on the cookie sheet for 2 minutes, then remove to a wire rack to finish cooling.