Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. In a large bowl, mix the peanut butter, sugar, egg, vanilla, and salt until a thick dough forms.

Roll the dough into 1-inch balls and place them on the baking sheet. Press each one with a fork to make a crosshatch pattern, flattening slightly. Bake for 8 to 10 minutes, until the edges are set.

Remove the sheet from the oven and immediately press a mini peanut butter cup into the middle of each hot cookie. Let them cool on the sheet for 5 minutes, then transfer to a wire rack.