Place the basil and garlic in the work bowl of a food processor. Process, scraping down the sides of the bowl as needed, until finely chopped. Add flour and salt; pulse to combine.
Add butter. Pulse about 10 times, or until the mixture resembles pea-sized crumbs.
Add water, 1 tablespoon at a time, pulsing several times after each addition. After 4 tablespoons water have been added, process the dough for several seconds to see if the mixture forms a ball. If not, add remaining water. Process until dough forms into a ball. Remove dough from processor.
Flatten the dough into a 5-inch disk. Wrap it in plastic, and refrigerate for at least 1 hour. (The dough can be tightly wrapped in plastic wrap and placed in a zipper-lock plastic bag then refrigerated for several days or frozen for 1 month. If frozen, defrost the dough in the refrigerator.)
Roll out the dough on a lightly floured surface into a 12-inch circle. Lay the dough over the tart pan, and press it into the pan. Trim the dough, and proceed with the recipe as directed.