Charleston Omelet Bar

Name: Charleston Omelet Bar
Ingredients: 1 tablespoon oil, or more as needed; 6 tablespoons unsalted butter; 1 large white onion, diced; 1 small green bell pepper, diced; 1 small red bell pepper, diced; 1/2 pound raw large (31/35) or extra-large (26/30) shrimp, peeled and deveined; 2 teaspoons seafood seasoning; 2 teaspoons fresh lemon juice; 1/2 pound lump crabmeat; 1/4 pound Havarti cheese slices; 1/4 pound Cheddar slices; One 8-ounce package sliced fresh mushrooms; 2 cups diced ham; 3 green onions, sliced; Chopped fresh parsley, for sprinkling; Chopped fresh dill, for sprinkling; 1 dozen large eggs; 1/2 cup whole milk; 1/2 teaspoon kosher salt; 1/2 teaspoon freshly ground black pepper