How to Make It
In a 12-inch ovenproof nonstick frying pan, melt 1 tablespoon of the butter over moderate heat. Add the scallions and cook, stirring, for 1 minute. Add the spinach, dried tarragon, if using, and 1/8 teaspoon each of the salt and pepper. Cook, stirring frequently, until the liquid evaporates, about 3 minutes. Remove the spinach mixture and let cool. Wipe out the pan.
In a large bowl, beat the eggs with the remaining 1/8 teaspoon each salt and pepper. Stir in the spinach mixture and fresh tarragon, if using.
Heat the broiler. In the same frying pan, melt the remaining 1 tablespoon butter with the oil over moderate heat. Pour in the egg mixture and reduce the heat to low. Sprinkle the feta over the top and cook until the bottom is golden brown and the top is almost set, 6 to 7 minutes. Broil the frittata 6 inches from the heat, if possible, until the eggs are set, 2 to 3 minutes.
Lift up the edge of the frittata with a spatula and slide the frittata onto a plate. Cut into wedges and serve.
Test-Kitchen Tip If the handle of your frying pan isn't ovenproof, protect it from the heat of the broiler by wrapping it with about four layers of aluminum foil.