In a medium bowl, toss together both cheeses and the flour. Heat a large nonstick skillet over a low to medium flame and sprinkle 1 1/2 tablespoons of the cheese mixture onto the pan to form a 4-inch circle. Sprinkle some thyme over the cheese and cook until the cheese is somewhat melted but not firm. Using a spatula, turn the cheese over and cook until firm and golden.
Transfer the frico to a paper towel, then quickly drape over a large rolling pin until completely cooled, to form a shell shape.
To serve, remove from pin and top each frico with arugula salad.
In a small bowl, whisk together lemon juice, shallots, mustard, and honey. Whisk in the olive oil and add salt and pepper, to taste. Lightly dress arugula leaves with the vinaigrette.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.