Position a rack in the center of the oven and heat the oven to 375°F. Bring a large pot of well-salted water to a boil over high heat.
Cook the spaghetti in the boiling water according to package directions. Drain well and let cool. Transfer to a medium bowl.
In an ovenproof 10-inch nonstick skillet, heat 1 Tbs. of the olive oil and 1/2 Tbs. of the butter over medium heat. Add the shallots and a pinch of salt and cook, stirring occasionally, until the shallots are softened and lightly golden, about 8?minutes. Add the arugula and toss with tongs until wilted, about 1 minute. With a heatproof spatula, scrape the arugula mixture and any fat left in the pan into the bowl with the pasta. Toss lightly to combine.
In a large bowl, whisk the eggs, cream, 1/2 tsp. salt, and several grinds of pepper. Add the pasta mixture, Parmigiano, mint, parsley, and chives. Mix gently but thoroughly.
Heat the remaining 1 Tbs. oil and 1/2 Tbs. butter in the skillet over medium-high heat. When the butter has melted and is bubbling, add the egg mixture. Use the heatproof spatula to gently distribute the ingredients evenly. Reduce the heat to medium low and cook until the eggs have set just along the outside edge of the pan, 4 to 5 minutes. Transfer the skillet to the oven and bake until the frittata is puffed, golden, and set, 22 to 24 minutes.
Let the frittata cool in the pan for 15 to 20 minutes. Run the spatula gently around the edge and underneath the frittata, and slide it onto a cutting board. Let sit for 5 to 10 minutes. Cut into wedges and serve.
nutrition information (per serving):
Photo: Scott Phillips