Preheat the oven to 375 degrees F.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the sliced potatoes to the skillet, saute for about 6 to 8 minutes, until tender but firm. Remove the potatoes from the skillet. Add another tablespoon olive oil, and add the green onions, tomatoes, spinach, and garlic. Saute for an additional 1 to 2 minutes or just until the spinach is wilted. Season the vegetables with salt, and pepper.
In a medium bowl, beat together the eggs, basil, cheese, salt, and pepper. Pour into the skillet over the vegetables. Reduce heat to medium-low and scramble the eggs for 1 minute. Return the potatoes to the skillet. Cook for an additional 2 to 3 minutes, 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 to 12 minutes, until the eggs have completely set in the center. Serve straight out of the skillet, or flip onto a serving plate. Garnish with shredded Asiago cheese and fresh basil.