Combine the eggs, egg whites, cheese, tarragon, salt, and pepper in a large bowl, and whisk to blend.
Set aside while you prepare the vegetables.
Heat 1 tablespoon of the olive oil in a large, oven safe skillet over medium high heat.
When hot, add in the diced vegetables and cook, stirring for 5-7 minutes, or until just tender, with golden brown edges.
Season with a pinch of salt and pepper.
Remove the vegetables and set aside in a bowl.
Heat the broiler.
Wipe out the pan with a paper towel and turn the heat down to medium-low.
Add the remaining 2 tablespoons of olive oil and swirl to coat the pan.
When the pan is hot, pour in the egg mixture and cook for about a minute, then gently spoon the vegetables over the eggs (do not mix them in).
Continue cooking until the edges have set.
Lift the frittata gently to see that the bottom has browned, about 5 minutes.
Put the skillet under the broiler for 2 minutes, or until the top is set and lightly browned.
Watch carefully to prevent burning.
Let the frittata cool for a few minutes.
Then slide it onto a serving plate, cut into wedges, and serve.