How to Make It
In a large saucepan, heat the oil to 300°. Fry the potatoes until softened but not browned, 10 minutes. Spread the fries on a paper towel–lined baking sheet.
Heat the oil to 350°. Line a large bowl with paper towels. Add the fries to the hot oil and cook until golden brown and crisp, 6 minutes. Transfer the fries to the bowl. Sprinkle the fries with the chopped herbs and salt and toss gently. Transfer to plates and serve right away with the burgers.
Meanwhile, preheat a grill pan. Form the meat into 4 patties and season generously with salt. Grill over moderately high heat, turning once, about 3 minutes per side for medium-rare meat. Transfer the burgers to the buns, top with 2 slices each of the Cambozola and the arugula and serve.