Preheat oven to 350 degrees. In a food processor, finely grind almonds, sugar, and salt. Add egg whites and vanilla; pulse until a ball forms.
With wet hands, shape level tablespoons of dough into little balls (dough will be very sticky). Place on parchment-lined baking sheets; flatten slightly. Use moist finger to make an indentation in the center of each cookie. Bake until crackly and light golden, 15 to 20 minutes.
Cool 5 minutes; transfer to a rack. Meanwhile, warm jam over low heat or in microwave in 10-second intervals until slightly liquefied and easy to spoon. Spoon jam filling into each cookie. Let set, about 5 minutes.