Preheat oven to 400 degrees. Line two baking sheets with parchment paper or silicone baking mats and set aside.
In a large bowl, stir together the flour, salt, 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 and 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 1/4-1/8" thick. Cut out into any desired shapes and place on prepared baking sheet. Prick with a fork and bake 10-12 minutes or until edges start to brown. Cool crackers on the baking sheet and serve.