Preheat the oven to 200° C. Heat the oil in a 10-inch cast-iron skillet over medium-high heat.
While the oil is heating, whisk the eggs in a large bowl with 1/2 cup each of the ricotta cheese, pesto and Parmigiano Reggiano cheese. Season generously with salt and pepper.
Reduce the heat to medium, pour the mixture into the skillet and cook until the edges are set but the center is still jiggly and uncooked, 7-8 minutes. Transfer to the oven and finish cooking until the top is puffed and set, another 5-6 minutes.
Remove from the oven, let rest 5 minutes and cut into wedges. Serve warm or at room temperature, dolloped with the remaining pesto and ricotta and garnished with the remaining Parmigiano Reggiano cheese.