If using a food processor: measure out flour, sugar, and salt in the bowl of a food processor and pulse a couple times to combine.
Cube butter and cream cheese and add to food processor along with chopped basil1. Pulse until butter and cream cheese form slightly smaller than pea sized pieces.
Add 3 tablespoons of cold water and pulse 2 to 3 times. Add more water 1 tablespoon at a time until larger pieces start to form, but dough should not come all the way together. Test dough by squeezing a ball of the mixture in your hand. If it holds together and does not crumble again when touched it is ready.
If using a pastry cutter: measure out flour, sugar, salt, and chopped basil into a large bowl. Add cubed butter and cream cheese and cut with your cutter until smaller than pea sized pieces form. Add water 1 tablespoon at a time, mixing with your hands until dough start to come together, and holds its shape when squeezed.
Empty the bowl onto a floured surface and form the dough into 2 disks with your hands. The dough will be crumbly but should mostly hold together. Wrap the disks in plastic wrap and refrigerate for 20 to 30 minutes.