Set the oven rack to the center position—Preheat to 350ºF (177ºC).
Line three large baking sheets with parchment paper.
In a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium-low speed (setting 4) until light and fluffy, about 1 minute.
Add the egg, vanilla, and salt. Mix on medium speed (setting 5), scraping down the sides of the bowl halfway through, 1 minute.
Gradually add the flour in three additions, mixing on low speed (stir) until just blended, do not overmix. The dough should be firm and not feel too sticky.
Roll the dough into 1 tablespoon (22g) sized balls.
Transfer the cookies to the parchment paper-lined baking sheet. Leave 2-inches of space in between.
Use your thumb, a measuring spoon, or the end of a wooden spoon to gently make an indent in the center of each cookie. They should flatten to about 1 ½-inches in diameter. Gently flatten the top if needed.
Stir the jam, then add it to a small resealable plastic bag or piping bag. If using thicker preserves, use a small measuring spoon to scoop into the cookie.
Cut the tip off the bag, then pipe a small amount of jam to fill the indent in each cookie, about ½-teaspoon.
Bake one tray at a time until cookies lightly brown around the edges, and on the bottoms, the surface will stay pale in color, 12 to 14 minutes.
Cool for 5 minutes on the pan, then transfer to a wire rack to cool completely.
Make-ahead: The dough can be made, rolled, indented, and stored in the refrigerator in an airtight container for up to 7 days. Place on prepared baking sheets, and let them sit at room temperature for about 15 minutes before baking.
Storing: Store in an airtight container for up to 7 days.
Freezing: Baked cookies can be placed between parchment paper and stored in an airtight container or resealable plastic bag for up to 3 months. The shaped dough can be frozen for 3 months and defrosted before baking.