Preheat your oven to 375°F and thoroughly coat a 9×13-inch baking dish with non-stick cooking spray. Drop the sliced sweet onions into a deep saucepan and add just enough cold water to cover them completely.

Bring the water to a rolling boil over high heat, then drop the flame down to medium-low to maintain a gentle simmer for 6 to 8 minutes. Watch the clock carefully and pull the pan the exact moment you can easily pierce an onion strand with a fork; over-cooking at this stage will cause the vegetables to collapse into a watery, structural mush later in the oven.

Empty the contents of the pan into a large colander in the sink, letting the onions sit undisturbed for 5 minutes to ensure every single drop of surface water drains away. Return the hot, bone-dry onion slices to the empty warm pan, drop in the 2 tablespoons of unsalted butter, and toss gently until the melting fat completely glazes the warm vegetable tissue.

In a separate large mixing bowl, combine the 3 eggs and evaporated milk, whisking aggressively for 45 seconds until smooth, frothy, and unified. Add the buttered onions, 1 cup of the cracker crumbs, the shredded sharp cheddar and mozzarella cheeses, salt, and black pepper into the egg wash, folding the ingredients together until the elements are suspended in the dairy base.

Transfer the wet onion mixture into your prepared 9×13-inch baking dish, smoothing the top surface into a flat, level sheet. In a small separate bowl, combine the remaining 1 cup of cracker crumbs with the 3 tablespoons of melted butter, tossing with a fork until the crumbs resemble damp sand, and sprinkle this mixture uniformly across the top of the casserole.

Place the pan uncovered on the middle oven rack and bake at 375°F for 40 to 45 minutes. Remove from the heat the second the internal egg custard completely sets without any fluid rippling in the center and the buttery top crumbs turn a deep, shaggy golden brown. Let the casserole rest on the counter for 5 to 10 minutes to allow the cheese lipids to stabilize and tighten before cutting into squares.