Cream butter in a large bowl with an electric mixer or stand mixer. Add powdered sugar and beat on low until a crumbly, sandy mixture forms. Gradually add salt and flour, 1 cup at a time, while mixing on low speed. The dough may look extremely dry and crumbly at this point.

Mix in eggs, egg yolks, and vanilla initially using the mixer, then finishing with your hands to create a smooth, soft, and pliable dough. Gather dough into a ball and refrigerate in a covered container for about 2 hours.

Preheat the oven to 350°F (180°F). Adjust the oven racks to the 2 middle rungs. Line 2 mini muffin tins with paper liners.

Using a small (1 ½ tablespoons) cookie scoop, measure out portions of the dough and set into the prepared muffin cups. Gently roll each dough portion into a smooth ball between your hands and place back into the muffin cups. Push a deep well into each ball using the wooden handle of a spatula or your finger. Fill wells with jam using a small spoon or a piping bag.

Bake cookies in the preheated oven until the tops of the cookies look dry, but not browned, 13 to 15 minutes. Swap trays halfway through or bake one at a time.