Preheat oven to 350°F (180°C). Line two baking sheets. Cream butter, peanut butter, and sugars until fluffy, about 2 minutes. Beat in egg and vanilla. Mix flour, cornstarch, baking soda, and salt separately, then stir into wet mixture until just combined.

Scoop dough into 1 ½ tablespoon balls, place 2 inches apart. Press a deep indent into the center of each with your thumb or a teaspoon.

Spoon about ½ teaspoon of jam into each indent, filling just below the rim.

Bake 10 to 12 minutes until edges are set and barely golden. Cool on sheet 5 minutes, then transfer to a rack to cool completely.