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1
Preheat oven to 400u00b0F.
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2
Crack the eggs and whisk together with the Parmigiano Reggiano, 1 teaspoon salt, and black pepper, and set aside.
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3
Trim 1/2 inch off the stem of the broccoli. Using a knife, separate all the florets from the base leaving the stem attached and then cut floret pieces in half (you can cut any especially large ones in quarters so all are evenly sized). In a 10- to 11-inch oven-safe saute pan over medium-high heat, cook the broccoli in 4 tablespoons of olive oil. Let the broccoli develop a nice brown color on one side, then turn everything over and season to taste with kosher salt.
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4
Transfer the pan to the oven and roast the broccoli until tender, 10 to 15 minutes. In a separate 10- to 11-inch saute pan, cook the onion in 2 tablespoons of olive oil, adding kosher salt to taste. Cook the onions for about 3 to 5 minutes over medium-high heat until lightly browned. Reserve onions on the side.
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5
Once the broccoli is fully roasted and tender, transfer the saute pan back to the stovetop and reduce the oven temperature to 300u00b0 F.
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6
Over medium heat, add 1 tablespoon of olive oil to the broccoli pan and add the garlic and chile. Cook the garlic and chile for 1 minute carefully so as not to burn the garlic. Add the cooked onions to the saute pan with the broccoli and mix well. Add the egg and cheese mixture and let cook for 30 seconds over high heat.
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7
Transfer the pan to the 300u00b0 F oven and let the frittata cook until the eggs are just set. Should be about 25 to 30 minutes. Remove the pan from the oven and then turn the frittata out with a rubber spatula onto a serving plate. Squeeze lemon juice over the top, drizzle extra virgin olive oil, and sprinkle with Parmigiano Reggiano to taste.
