Combine the butter, peanut butter and brown sugar in the bowl of a stand mixer. Beat on medium speed until light and fluffy. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla extract.
In another bowl, whisk together the gluten-free flour, xanthan gum, baking soda and salt. Add this mixture to the peanut butter mixture and beat until just combined. Transfer the dough to a piece of plastic wrap and cover it. Refrigerate for at least one hour or overnight.
Pre-heat oven to 375°F. and Line a baking sheet (or several, if you have them!) with parchment paper. Use a medium cookie scoop to scoop tablespoons of dough onto the cookie sheet. Use a thumb or the handle end of a wooden spoon to make a divot in the center of each cookie. Bake for 7-9 minutes or until puffed and mostly set.
If the divots rise too much during baking, just use your thumb to press them back down as they cool.
Allow the cookies to cool completely, then fill each divot with about a 1/2 teaspoon of jam. Depending on the thickness of your jam, you may want to microwave it for ten seconds to make filling easier.