Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper. Whisk the flour, baking powder and salt in a bowl. Beat the butter, granulated sugar and vanilla in a large bowl with a mixer until light and fluffy. Add half of the dry ingredients and mix until just combined, then mix in the remaining dry ingredients. Knead a few times by hand to bring the dough together.
Roll teaspoonfuls of dough into balls and place about 1/2 inch apart on the prepared baking sheets. Make an indentation in the center of each ball with a small measuring spoon or the back of a pen. Fill each indentation with jam (a scant 1/8 teaspoon).
Bake until the edges of the cookies are golden, 15 to 20 minutes. Let cool 2 minutes on the baking sheets, then transfer to a rack to cool completely. Dust with confectioners' sugar, if desired. Store in an airtight container up to 1 week.