Heat broiler and place oven rack in center of oven.
Heat EVOO and butter in a large ovensafe skillet over medium to medium-high heat. Add shallots, potatoes, celery and garlic to the pan. Season with black pepper and sauté 6-7 minutes, until tender. Add tuna and stir to combine.
In a bowl, beat eggs with hot sauce, milk or half-n-half. Pour eggs into the skillet and stir in herbs. Let the eggs set and brown along the edges and on the bottom. Transfer to oven and brown top lightly, 5 minutes. Top with cheese and return to broiler to melt, 1-2 minutes. Cut into wedges and serve with buttered English muffins alongside.