Place racks in top and bottom thirds of oven; preheat to 350ºF. Line 2 large baking sheets with parchment.
In a bowl, whisk flour, baking soda and salt. In a large bowl, using an electric mixer on low speed, beat peanut butter, sugar, egg, 1/4 cup water and vanilla until combined. Increase speed to medium and beat until mixture is well-blended and light, about 3 minutes. On low speed, gradually beat in flour mixture until just incorporated.
Pinch off a heaping teaspoonful of dough and roll into a 1-inch ball. Place on a baking sheet. Repeat, covering both sheets, spacing dough balls 1 inch apart. With end of a wooden spoon handle, make an indentation in center of each ball. Fill each indentation with 1/4 teaspoon jam.
Bake, switching sheets halfway through, until lightly browned, about 12 minutes. Let cool on sheets on wire racks for 2 minutes, then transfer to wire racks to cool completely. Repeat with remaining dough and jam.