Directions

1. In a medium bowl, stir together the cheddar, the Jack, the Parmesan, 1/2 cup of the mayonnaise, and the tarragon until evenly mixed.
2. Divide the cheese and mayonnaise mixture among 4 slices of bread and gently spread to cover evenly to the very edges. Place the 4 remaining slices of bread on top to form sandwiches and press gently but firmly.
3. In a wide, shallow bowl, whisk the eggs, the milk, the remaining 1/4 cup mayonnaisie, the thyme, and salt. Mix until smooth and set aside.
4. Preheat oven to 325°. Dip the sandwiches into the egg mixture one by one to coat, and set aside. In a 12- to 14-inch nonstick sauté pan, heat 1 Tbsp. of olive oil until smoking. Add 1 Tbsp. of the butter and heat until the sizzling subsides.
5. Place 2 sandwiches in the pan and cook slowly until golden brown on the first side, about 3 minutes, then flip each sandwich and cook on the other side for 3 more minutes. Remove sandwiches to a baking pan and place in oven. Repeat the process with the remaining oil, butter, and sandwiches. Leave sandwiches in oven 10 minutes and then serve.