Step 1Place the cheese in the freezer for 5 minutes. Cut it into thick slices. Dredge in the flour, then in the beaten egg and finally in the panko crumbs, pressing to coat well on all sides. Set aside on a plate (in the refrigerator if doing ahead).
Step 2Combine the greens and herbs in a large bowl and toss well until completely mixed. In a small bowl, whisk together the vinegar and olive oil and season with salt and pepper. Set both bowls aside.
Step 3Heat the butter and oil in small skillet over medium-high heat until sizzling. Carefully add the cheese slices and cook quickly until lightly browned on each side but not starting to ooze, about 1 minute.
Step 4As the cheese heats, toss the salad with the dressing to coat and divide among 4 plates. Top each with hot cheese and serve at once.