Set a rack in the upper third of the oven; preheat to 450 degrees F. Whisk the eggs in a large bowl until foamy. Heat 1 tablespoon olive oil in a large nonstick ovenproof skillet over medium-high heat. Add the mushrooms and cook, stirring occasionally, until golden, 3 to 4 minutes. Reduce the heat to medium. Add the butter, scallions, parsley, tarragon, 1/4 teaspoon salt and a few grinds of pepper. Cook until the scallions are wilted, about 3 minutes.
Pour the beaten eggs into the skillet in an even layer and cook until they start browning, about 3 minutes; sprinkle with the cheese. Transfer the skillet to the oven and bake until set, about 5 minutes.
Meanwhile, combine the endive and tomatoes in a bowl. Add the lemon juice, the remaining 2 tablespoons olive oil, and salt and pepper. Toss and serve with the sliced frittata.