With all of your chicken pounded out, place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. While that's heating up, set up two dishes on the counter: Fill one the egg whites and the other with about a cup of the Parmigiano Reggiano. Season the chicken cutlets on both sides with salt and freshly ground black pepper, then dip them first in the egg white and then in the grated cheese.
Once all of your cutlets are coated, cook them in the hot pan until golden brown and cooked through, 3-4 minutes per side. When they're finished, reserve them to a plate while your veggies are cooking.
As soon as you drop your chicken cutlets into the pan, drop your pasta and cook to al dente according to package directions (just before draining the pasta take a scoop of the starchy cooking water out and save it to make your sauce with).
Place another large skillet over medium-high heat with 1 turn of the pan of EVOO, about 1 tablespoon. Toss the scallions, garlic and parsley into the pan and cook until tender, about 1 minute. Add the lemon zest and juice, artichoke hearts, remaining Parmigiano Reggiano and your scoop of starchy pasta water (you're looking for about 1 cup of liquid here). Hit the pan of veggies with a little salt and freshly ground pepper, and cook for about 1 minute to heat everything through.
While that's coming up to a bubble, drain your pasta and toss it into the pan with the sauce to heat up along with it. Just before you're ready to serve, toss the spinach in the pan too and give it a light toss to coat – you don't need to worry about "cooking" this too much, the heat from everything in the pan will wilt the spinach perfectly.
Once everything's heated through, divide the pasta mixture between four plates and top each portion with a crispy crusted chicken cutlet.