Crack the eggs into a medium bowl; add the Parmigiano Reggiano, fine salt, and black pepper. Whisk until the mixture is smooth and slightly frothy, 30β45 seconds.
Heat 2 tbsp extra-virgin olive oil in a 10-inch nonstick or well-seasoned skillet over medium-low. Add the spring onions and cook, stirring occasionally, until tender and sweet but not browned, 6β8 minutes.
Spread the onions evenly in the skillet and reduce the heat to low. Pour the egg mixture over the onions. Stir gently for 10β20 seconds to distribute, then smooth the surface.
Cook undisturbed until the edges are set and the center is mostly set with a slight wobble, 4β6 minutes, loosening the sides with a spatula as it cooks.
Slide the frittata onto a plate. Add 1 tbsp extra-virgin olive oil to the skillet. Invert the plate to flip the frittata back into the skillet, uncooked side down, and cook until just set and lightly golden, 1β2 minutes.
Slide onto a board or plate and let rest 2 minutes. Cut into wedges and serve warm or at room temperature.