Preheat the oven to 425 degrees F. Grease a 9×13-inch baking dish with butter.
Make the breadcrumbs: In a food processor, process the white sandwich bread until it forms fine crumbs (you should have about 4 cups). In a large skillet, heat 6 tablespoons unsalted butter over medium-low heat; when it foams, add the minced garlic and cook, stirring, until fragrant but not browned, 1 to 2 minutes. Add the bread crumbs, increase the heat to medium, and cook, stirring frequently, until toasty and browned, 7 to 9 minutes. Stir in 1 teaspoon kosher salt and 1/2 teaspoon black pepper, remove from the heat, transfer to a large plate to cool for 5 minutes, then stir in 5 tablespoons grated Parmesan cheese.
Cook the pasta: In a large pot of salted boiling water, cook 1 pound pasta shells according to the al dente directions on the package (if not included, cook for one minute less than called for). Drain, rinse, and toss with 1 teaspoon olive oil to prevent sticking.
Make the cheese sauce: In a large saucepan or Dutch oven, heat 1/2 cup (113.5g) unsalted butter over medium-high heat until melted. Add 5 tablespoons all-purpose flour and cook, constantly whisking, until it turns a light and toasty brown color, 3 to 6 minutes. Gradually add 5 cups whole milk while whisking, then increase the heat to high and bring to a boil. Reduce the heat to medium and cook, whisking, until it thickens, 4 to 5 minutes. Add the cheeses (12 ounces cheddar, 12 ounces Swiss or Gruyere, and 12 ounces American) a few handfuls at a time and whisk until the sauce is smooth. Whisk in 2 teaspoons kosher salt, 1/4 teaspoon black pepper, and 1/4 teaspoon cayenne pepper. Stir in the cooked pasta and season to taste with more salt and pepper.
Assemble and bake: Pour the macaroni and cheese mixture into the buttered 9×13-inch baking dish and spread the breadcrumbs evenly over the top. Bake until the topping is browned and crisp and the cheese is bubbling, about 8 to 10 minutes. Leftovers can be stored, covered, in the refrigerator for up to 4 days.