Move the rack toward the top of the oven and preheat to 325 degrees F. Grease a 2-quart baking dish with 1 tablespoon of butter.
Sauté onion until lightly browned. Be careful not to burn.
Whisk the eggs and milk together in a large bowl. Add the corn, 1 sleeve of the coarsely crushed Ritz crackers, 1 cup of the extra sharp cheddar and 1 teaspoon salt. Pour the mixture into the baking dish, use a spatula to make an even layer.
Bake uncovered until the edges are set, but the center is still wet (not set), about 35 minutes. Meanwhile, melt the remaining 3 tablespoons butter in a small dish in the microwave, about 25 seconds. Mix the butter into the remaining 1 cup crushed Ritz crackers until evenly moistened. Sprinkle Pecorino Romano cheese and the buttered crackers over the corn. Continue baking until the top is set and golden brown (the center should puff up), approximately 20 to 25 minutes more. To confirm that it is done, put a toothpick in the center and make sure it comes out clean.If you find that the center is not done and the crust is already golden brown cover until it’s done to prevent the top from burning.
Remove from the oven and let stand 5 minutes before serving.
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