How to Make It
In a medium bowl, whisk the 2 flours with the salt. Mound the flour mixture on a work surface and make a well in the center. Add the eggs and olive oil to the well and beat with a fork; gradually incorporate the flour, starting with the inner rim and maintaining the side of the well as long as possible. Once a soft dough forms, knead until elastic and smooth but still a little tacky, about 5 minutes. Wrap the pasta dough in plastic and refrigerate for 1 hour.
Divide the dough in half. On a floured work surface, using a lightly floured rolling pin, roll out 1 piece of dough 1/16 inch thick. With a sharp knife, cut the dough into 2-inch-thick strips, then cut each strip into 2- to 3-inch triangles. Transfer to a parchment paper–lined baking sheet and top with another sheet of parchment. Repeat with the second piece of dough.
In a large skillet, cook the lardo over moderately low heat, stirring, until starting to crisp, 3 to 4 minutes. Add the garlic and cook until fragrant, 1 minute. Add the egg and cook, stirring, just until scrambled. Add the spinach and arugula and toss just until wilted, about 2 minutes. Season the topping with salt and pepper and set aside half in a bowl.
In a pot of salted boiling water, cook half of the pasta until al dente, about 3 minutes. Using a slotted spoon, add the triangles to the topping in the skillet with a little water clinging to the pasta. Add 1/4 cup of the cheese. Cook over moderate heat, tossing, until well blended, 2 minutes. Transfer to a large serving bowl. Repeat with the remaining pasta, boiling it, then finishing it with the remaining topping and 1/4 cup of cheese. Garnish the dish with cheese, drizzle with oil and serve.