Preheat oven to 350 degrees F. Line 2 baking sheets with parchment paper or silicon mats.
Whisk the flour, baking powder, and salt together in a bowl.
In another bowl, whip the butter and the sugar with a hand-held mixer until fluffy, about 5 minutes. Beat in the egg and vanilla until just combined. Slowly beat in the dry ingredients, in 2 additions, mixing just until incorporated.
Scoop the dough into 1-inch balls with a cookie or ice cream scoop and roll in sugar. Place about 2 inches apart on the prepared baking sheets. Press a thumbprint into the center of each ball, about 1/2-inch deep. Fill each print with about 3/4 teaspoon of jam.
Bake cookies until the edges are golden, about 15 minutes. (Rotate the pans, from top to bottom, about halfway through baking for even color.) Cool cookies on the baking sheets. Serve.
Store cookies in a tightly sealed container for up to 5 days.
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