Put 1 baking sheet on the center rack of the oven and preheat to 350 degrees F.
Slice 1/4-inch of the crust off the top and bottom of the loaf of bread. Split the loaf evenly in half, horizontally. Cut a piece of parchment paper large enough to accommodate both halves of bread and put both the top and the bottom on the parchment, cut-side up so the inside of the loaf is visible.
Scoop about a 1/4-inch of the soft middle of the loaf out. Spread the mayonnaise evenly on the crustless top of each half, then flip them over so the mayonnaise-side is face down on the parchment.
Evenly distribute the 3 cheeses between the 2 bread halves. Use the parchment to transfer your grilled cheese to the preheated baking sheet, using a spatula if the bread is sticking, then remove and discard the parchment. Bake until the crust is golden brown and crunchy and the cheese is melted, about 18 minutes. Remove from the oven and immediately sandwich the 2 halves with the cheese in the middle. Let rest about 10 minutes. Slice and serve while hot.
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