Dust artichoke hearts with flour, shaking off any excess.
Heat 6 tablespoons olive oil in a large skillet over high heat. Saute artichokes, stirring often, until lightly browned, about 8 minutes. Drain on paper towels. Discard oil.
Whisk eggs lightly in a bowl; season with salt and pepper.
Heat remaining 2 tablespoons olive oil in the skillet. Arrange artichokes in the skillet. Pour eggs over artichokes. Cook until lightly browned, 4 to 5 minutes. Flip omelet carefully and continue cooking until firm and lightly browned on second side, about 4 minutes more.
