Heat the oil in an 8-inch skillet set over medium heat. Add the tomatoes cut-side down to the pan and cook until charred, 1 minute. Gently shake the pan to toss the tomatoes, then saute for 1 minute. Add the scallions and saute for 1 minute. Add the spinach and saute until wilted, about 1 minute.
In a small bowl, add the eggs, salt and pepper, and whisk. Add the eggs to the pan, and cook until the edges begin to set, about 2 minutes. Gently lift the edge of the frittata, tilting the pan to allow any uncooked eggs to flow to the bottom of the pan. Cook until the frittata is almost set, 2 to 4 minutes.
Sprinkle the frittata with the feta and parsley. Serve hot.