Bring dates, water, and sugar to a boil. Reduce heat to low and simmer, stirring frequently, until dates are thickened, about 5 to 7 minutes. Set aside to cool (can be prepared the day before, if needed).
Cream butter and sugar with your mixer. Add in the egg, water and vanilla.
Stir together the flour, baking soda and salt. Gently blend the dry ingredients to the butter mixture.
Preheat oven to 350°F. Lightly grease your cookie sheet or use a silicone baking mat.
Drop cookie dough by teaspoonfuls onto a lightly greased cookie sheet or use a silicon mat. Place about 1/2 teaspoon of date mixture on the top of each cookie, then a small dab of cookie dough on top of the date mixture.
Bake at 350° for 10 to 12 minutes. Cool 5 minutes on cookie sheet before moving to a cooling rack.