Pillsbury has a recipe for date-filled cookies on its website. Called Grandma"s Date-Filled Cookies, the recipe is a sugar cookie recipe with a date-and-sugar filling.
In a large mixing bowl, beat 1 1/2 cups brown sugar with 1 cup softened butter until fluffy; then add 1 teaspoon vanilla and 3 eggs, beating until well-blended. To this mixture, add 3 1/2 cups flour and 1 teaspoon baking soda. Use an electric mixer on low to combine all ingredients. Cover the bowl with plastic wrap, and refrigerate for two hours.
Place 2 cups chopped dates, 1 cup granulated sugar and 1 cup water in a saucepan. Heat the mixture to boiling, and reduce the heat to low, simmering uncovered for 10 minutes and stirring often. Place the mixture in the refrigerator until the dough mixture is ready.
Preheat the oven to 350 degrees. Using one-third of the dough at a time, roll the dough into a 1/8-inch thick rectangle and then cut 2 1/2-inch-diameter circles out of the dough. Remove the center, about a 1-inch circle, from half of these circles, and place the other half on an ungreased cookie sheet.
Spoon 1 tablespoon of the date filling on top of each of the whole cookies and place the dough ring on top. Press the top and bottom edges together to form a tight seal. Repeat the process with the remaining dough and filling, working with one-third of the dough at a time. Bake for seven to 10 minutes, until golden brown.