Sams Carrot Souffle

Name: Sam's Carrot Souffle
Ingredients: 1 tablespoon unsalted butter, room temperature, plus more for baking dish; 2 pounds carrots, peeled and cut into 1/4-inch-thick rounds; Coarse salt; 1 cup whole milk; 1 cup saltine cracker crumbs; 3/4 cup grated sharp white cheddar cheese; 1/3 cup very finely chopped onion; 1/4 teaspoon freshly ground black pepper; 1/8 teaspoon cayenne pepper; 3 large eggs