In the bowl of a mixer, cream the butter and sugar until fluffy, about 2-3 minutes.
Add the flour and vanilla, mix well.
Empty the dough onto a large piece of plastic wrap, mushing it together into a solid disk using the plastic to help, then wrap well and refrigerate the dough for a half hour, no more than an hour.
Preheat the oven to 375° F (196° C) and lightly grease a cookie sheet with cooking spray.
Remove the dough from the refrigerator and pull off small pieces, about a scant (measuring spoon) tablespoon size, roll into balls, then flatten on the cookie sheet, less than a quarter inch thick.
Make a small indent in the middle of each cookie dough round with a thumb or spoon and scoop about a heaping half teaspoon size amount of preserves or jam into the indent.
Bake for 12-15 minutes, beginning to check at 10 minutes, or until lightly golden brown on the edges. Repeat until all the dough is baked. No need to re-grease the cookie sheet.
Remove to a cooling rack to cool completely and store in a tightly sealed container.