In a stand mixer, beat butter on high until fluffy, about 3 minutes. Add sugar and continue to beat until well combined, about another 2 minutes. Turn to low speed and slowly add the flour. Continue mixing until a dough is formed, about 2 more minutes.
Turn dough out onto a non-greased 9x9 baking pan. Evenly distribute dough throughout the entire pan. Place in oven and bake for 25-30 minutes, or until golden brown.
Remove from oven. Using a rubber spatula, make light perforations in the dough to create 16 even squares. Use the end of the spatula to create a "thumbprint" in the middle of each cookie.
Immediately fill each thumbprint with Sticky Sweet Tomatoes. Let cool completely before serving.