Preheat the oven to 375 degrees. Line two baking sheets with parchment. Sift together the flours, salt and sugar, and place in the bowl of a food processor fitted with the steel blade. Add the butter, and pulse until the mixture is crumbly. Add the cheese, and pulse several times to distribute it evenly throughout the flour mixture. Turn on the food processor, and add the olive oil and eggs. Stop the machine when the dough comes together. It will be soft and somewhat sticky. If it seems very moist, add another tablespoon of flour and pulse until incorporated. Lightly flour your hands and your work surface. Scrape out the dough and form two equal pieces. Shape into rounds, wrap in plastic and let rest for 15 minutes. Roll out each piece of dough between pieces of lightly floured parchment. Cut into squares or rectangles, and place on the parchment-lined baking sheets. Bake 15 to 20 minutes, switching the pans after the first 10 minutes from front to back and top to bottom. They will foam in the oven because of the cheese, but that will subside and they will bake crisply. The crackers are done when they are lightly browned. Remove from the oven, and cool on racks. Store in an airtight container.