Heat oven to 325°F. Line 2 baking sheets with parchment paper.
In a mixing bowl, beat the butter and powdered sugar on medium speed until creamy and smooth, 1 to 2 minutes. Mix in the lemon zest, vanilla, and salt until fragrant.
Add the flour and mix on low just until the dough comes together and looks like soft clumps. Do not overmix.
Scoop level tablespoon portions (about 18), roll into smooth balls, and space them 2 inches apart on the prepared sheets. Chill the shaped dough for 10 minutes to help hold the thumbprints.
Using your thumb or the back of a 1/2-teaspoon measure, press a deep well in the center of each ball. If edges crack, gently nudge them back together.
Stir the blueberry jam until glossy and loose, then spoon about 1/2 teaspoon into each indentation (do not overfill).
Bake 15 to 17 minutes, rotating the pans halfway, until the bottoms are lightly golden and the edges look dry. Cool on the sheet for 5 minutes, then transfer to a rack to finish cooling. If the centers settle, add a tiny dot more jam while warm.