Line 2 baking sheets with parchment paper or nonstick mats. In a large bowl, beat together the butter and powdered sugar until light and fluffy. Add the milk and vanilla, and mix well. Add the flour and salt. Beat together until the ingredients are completely incorporated and the dough comes together.
Scoop the dough by rounded tablespoonfuls onto your baking sheets. Use a 1/2-teaspoon measuring spoon to press into each cookie, making a divot in the center where the jam will go. Place the cookie dough in refrigerator for 30 minutes to chill.
Preheat oven to 325 degrees F. Take out the cookies and spoon the preserves into each divot, filling it to the top of the indent. Bake until the cookies have just started to brown, 20-22 minutes. Let cool completely on a wire rack and enjoy.