Preheat the oven to 350°F.
In a medium bowl, whisk the eggs until combined. Add the garlic, lemon juice, Parmigiano Reggiano, and season with salt and pepper. Stir until combined.
Heat the olive oil in a medium cast-iron skillet over medium-high heat. Add the egg mixture to the skillet. Arrange the squash blossoms and tomatoes over the top. Cook for 5 minutes.
Place the skillet in the oven and bake for 20 to 25 minutes. Remove from the oven. Sprinkle the basil over the top and slice into wedges. Serve immediately.