Using paper towels, pat oysters dry. Season the oysters with salt and pepper. Set aside.
Arrange three bowls. Add flour to the first, 1 beaten egg to the second and breadcrumbs to the third. Dip each oyster into the flour followed by the egg and the breadcrumbs. Place the prepared oysters onto a floured plate.
In a large skillet over medium-high heat, melt the butter. Fry the oysters until golden brown, flipping once, 6-8 minutes.
Whisk the remaining eggs in a bowl. Season the eggs with salt and pepper, to taste.
Add the seasoned eggs to the oyster mixture along with half the bacon and scallions.
Cook the mixture until the eggs have just set, about 3 minutes. Smooth the top, cover, and cook until the omelet is set, about 5 minutes.
Transfer the omelet to a serving plate, and garnish with the remaining bacon and scallions.
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