Preheat oven to 350°F. Line 2 baking sheets with parchment paper or silicone 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" balls with a cookie or ice cream scoop and roll in sugar. Place about 2" apart on the prepared baking sheets. Press a thumbprint into the center of each ball, about 1/2" deep. Fill each indentation with about 3/4 tsp jam.
Bake cookies until the edges are lightly golden, about 15 minutes. (For even color, rotate the pans from top to bottom about halfway through baking.) Cool cookies on the baking sheets. When cool, lightly sprinkle powdered sugar over top just to give it a dusting.
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