3/4 cup all-purpose flour
1/2 teaspoon salt
1 teaspoon coarsely ground pepper
1 teaspoon chopped fresh rosemary
4 tablespoons (1/2 stick) unsalted butter, chilled, cut into pieces
1 cup grated Parmesan cheese
1/4 cup heavy cream
4 tablespoons olive oil
sea salt for sprinkling
Combine flour, salt, pepper, and rosemary in the bowl of a food processor and pulse twice to mix. Add butter and pulse until the mixture resembles coarse meal, about 10 pulses. Add the cheese and pulse twice to combine. With the motor running, pour in the cream and continue processing until the dough forms a single mass. Transfer dough to a work surface and roll into a log about 2 inches in diameter. Wrap with plastic wrap and refrigerate for at least 3 hours or up to 2 days.
Preheat an oven to 325F. Line a baking sheet with silpat or parchment paper.
Roll out dough as absolutely thin as you can (less than 1/8 inch) and place the entire sheet on the silpat. Using a pastry wheel, cut crackers. Brush with olive oil and sprinkle with sea salt. Bake until the crackers are light golden brown, 18 to 20 minutes.
Transfer the baking sheet to a wire rack. When the crackers are cool to the touch, transfer them to the rack.