Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Combine the flour, Parmesan, rosemary, pepper, cayenne and 1/2 teaspoon salt in a food processor; pulse to combine. Add the butter and pulse until incorporated. Add the 1/4 cup heavy cream and process until the dough forms a ball. If a ball does not form, add more heavy cream, one tablespoon at a time, and process until the dough comes together.
Lightly flour a work surface. Pat the dough out in into a flat rectangle, then lightly flour the dough and roll it out until it is a little less than 1/4-inch thick and about 12-by-8-inches in size. Cut the dough into squares or rectangles and carefully transfer them to the prepared baking sheet. Sprinkle with 1/4 teaspoon salt, gently pressing the salt into the surface of the crackers.
Bake until light golden brown, 10 to 12 minutes. Cool completely on a rack.