Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper and spray with nonstick cooking spray.
Pulse the peanuts in a food processor until they are a fine meal. Add the oats, flour and salt and process until blended. Transfer to a bowl. In the food processor, combine the butter and sugar and process until light and fluffy. With the motor running, add the egg and vanilla. Process until smooth. Add half of the dry ingredients back into the processor and pulse to combine. Add the remaining half and pulse again until combined.
Drop the cookie dough by the tablespoonful (I use an ice cream scoop) onto the prepared baking sheets, leaving about 1 1/2 inches between the cookies. Use your thumb to make a thumb print in each cookie.
Bake until the bottoms of the cookies are lightly golden brown, 12 to 15 minutes. Cool on a wire rack.
Stir the jelly in a small bowl to loosen it up and fill each thumbprint with about 1 teaspoon.