10 large eggs 2 1/2 tablespoons grated Parmigiano Reggiano, plus more for serving 1 teaspoon kosher salt, plus more to taste 40 turns from a black pepper mill 7 tablespoons extra-virgin olive oil, divided, plus more for serving 1 medium (1-pound) head of broccoli (4 cups once trimmed) 1/2 of a red onion, sliced thinly 1 tablespoon chopped garlic (heaping) 1/8 teaspoon plus a large pinch of dried chile flakes 1 squeeze lemon, to taste, for serving Preheat oven to 400° F. Crack the eggs and whisk together with the Parmigiano Reggiano, 1 teaspoon salt, and black pepper, and set aside. 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 sauté 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. Transfer the pan to the oven and roast the broccoli until tender, 10 to 15 minutes. In a separate 10- to 11-inch sauté 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. Once the broccoli is fully roasted and tender, transfer the sauté pan back to the stovetop and reduce the oven temperature to 300° F. 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 sauté pan with the broccoli and mix well. Add the egg and cheese mixture and let cook for 30 seconds over high heat. Transfer the pan to the 300° 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.