Heat vegetable oil in a heavy-bottomed saucepan over medium to 360°F. Preheat broiler with rack 6 inches from heat.

Whisk together eggs, cream, chives, ¼ cup of the bacon, and ½ teaspoon each of the salt and black pepper in a large bowl. Set aside.

Place oysters in a shallow dish, and add buttermilk; stir to coat. Combine flour, cornmeal, cayenne, and ½ teaspoon of the salt in a medium bowl. Dredge half of the oysters in flour mixture; shake off excess. Fry in hot oil until golden brown and floating, 2 to 3 minutes. Drain on paper towels. Repeat with remaining oysters. Sprinkle with remaining ½ teaspoon each salt and black pepper.

Heat butter in an 8-inch nonstick skillet over medium. Pour egg mixture in skillet. Cook until bottom is set, about 1 minute. Using a rubber spatula, gather set edges to middle of skillet, and let liquid run out of the middle. Place skillet under broiler, and broil until top and center are just set, 30 seconds to 1 minute. Slide omelet onto a platter or cutting board.

Toss together frisée, lemon juice, and olive oil in a large bowl. Top omelet with frisée and oysters; sprinkle with remaining ¼ cup bacon. Serve immediately.