Line two baking sheets with parchment paper. Whisk the blackberry jam in a small bowl until loosened and spreadable.

In a large bowl, beat butter and sugar on medium speed until light and fluffy, about 3 minutes. Scrape down the bowl. Beat in egg yolk and vanilla until just combined, about 30 seconds.

Add flour and salt. Mix on low speed until dough comes together in clumps, then finish mixing by hand with a spatula until no dry flour remains. Do not overmix.

Scoop dough into 1-tablespoon portions and roll into balls. Roll each in granulated sugar to coat lightly. Place 2 inches apart on prepared sheets. Use your thumb or the back of a 0.5-teaspoon measuring spoon to press a deep well in the center of each, almost to the bottom but not through.

Freeze the shaped cookies on the baking sheets until firm, about 30 minutes. This prevents spreading and helps the thumbprints hold their shape.

Preheat oven to 350F. Bake one sheet at a time for 10 minutes until puffed and just set but still pale on top. The indentations will have puffed slightly.

Remove from oven and immediately redefine the wells with the back of your measuring spoon if needed. Fill each with about 0.5 teaspoon of jam. Return to oven and bake 4 minutes more until the cookies are very lightly golden at the edges. Let cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.