Preheat oven to 400° F. Line two baking sheets with parchment paper or silicone baking mats and set aside.
In a large bowl, stir together the flour, salt, black pepper, and basil. Stir in grated cheese.
Blend softened butter the into dry ingredients until well incorporated (no big lumps). Stir in heavy cream one tablespoon at a time until larger clumps start coming together. Mixture should come together into a dough ball that isn't sticky.
Roll onto a lightly floured board to be 1/8-1/4" thick. Cut out into any desired shapes and place on prepared baking sheet. ackers on the baking sheet and serve.
Prick each cracker with a fork once, and bake 10-12 minutes or until edges start to brown. Cool crackers on baking sheet, then serve as desired.