Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the vegetables to the skillet, saute for about 6 to 8 minutes, until tender but firm.
In a medium bowl, beat together the eggs, cheese, salt, and pepper. Pour into the skillet over the vegetables. Reduce the heat to medium-low and scramble the eggs for 1 minute, or just until the eggs start to set around the edges. Drizzle olive oil around the edge of the pan to ensure easy removal.
Finish cooking in the oven for an additional 10 to12 minutes, until the eggs have completely set in the center. Serve straight out of the skillet, or flip onto a serving plate. Garnish with more shredded cheese.