In a large mixing bowl, cream butter and sugar together with an electric mixer until well combined. Beat in the vanilla.
In a medium size mixing bowl, stir together the 3 1/2 cups flour and salt. Add to the butter mixture, and beat on a low speed until ingredients are combined. Place dough onto a lightly floured surface and shape into a disc, (I shaped 2 discs for easier handling)
Wrap in cling wrap and chill about 45 minutes to an hour.
Roll the dough out about 1/2 inch thick, dip cookie cutters in flour, and cut shapes. (For these cutters, press down the main cutter and the press the plunger that is in the center. It takes a few tries to press correctly and not too hard)
Place cookies on parchment lined baking sheets, chill about 10 minutes.
Fill center with desired flavored preserves.
Bake about 12 minutes. Remove from oven before cookies are light golden brown and allow to set on cookie sheet. Remove to cooling rack. Makes about 48 cookies.