Preheat oven to 375º.
Whisk together eggs, salt, pepper and freshly grated Parmigiano-Reggiano.
Peel the potato and slice into 1/4 inch rounds.
Place the cut potato into boiling salted water and blanch for 3 minutes, drain and transfer to a bowl of ice water.
Slice the onion into thin slices.
Add 2 tablespoons of oil to a heavy, oven-proof 12-inch skillet that is 2 inches deep. Heat oil over medium heat.
Add the sliced onion to the skillet and cook until soft, and caramelized.
Transfer to a bowl and set aside.
Drain potatoes and pat them dry.
Layer potatoes in the skillet overlapping them and cook over low heat for 1 minute.
Add the caramelized onions evenly on top of the sliced potatoes.
Pour the egg mixture over the potatoes and onions.
Sprinkle 1/2 teaspoon of thyme and reserve the other half for garnish.
Cook over low heat until the eggs are almost set, about 5 minutes.
Transfer to the oven and cook for 15 to 20 minutes or until golden and firm.
Put a serving plate on top of the skillet and flip so the frittata released from the pan and onto the plate.
Let it rest for 5 minutes, garnish with the remaining thyme, then slice and serve.