Prepare parmesan crusted chicken. Season both sides of the chicken cutlets with salt and pepper. Put ½ cup flour in one shallow bowl, 2 whisked eggs in another, and 1 cup panko with ¼ cup parmesan in a third bowl. Dredge chicken in the flour, shaking off excess. Dip chicken in egg and coat in panko and parmesan mix.
Heat ¼ cup oil in a saute pan over medium heat. Cook chicken until golden brown, about 3-4 minutes. Flip and cook on the other side until juices run clear. Remove chicken from the pan and keep warm.
Wipe the pan clean and heat 1 tablespoon oil. Add brussels sprouts and cook until charred, about 4-5 minutes. Add garlic and saute another minute. Season with salt, pepper, and red pepper flakes. Remove brussels sprouts from pan and set them aside.
Bring a pot of salted water to a boil over high heat. Cook spaghetti until al dente, about 8 minutes. Drain, reserving ¼ cup of the cooking water.
Meanwhile, melt 2 tablespoons in the same pan and lay lemon slices in an even layer. Cook until caramelized, about 2 minutes. Flip and brown on the other side. Add tablespoon and saute until browned, about 30 seconds.
Add white wine and bring to a simmer. Continue to cook for 1 minute. Add chicken stock and juice of ½ lemon and bring to a simmer. Continue to cook for 5 minutes over medium heat. Season sauce with salt and pepper.
Add spaghetti, Brussels sprouts, ¼ cup reserved pasta water, 1 cup parmesan, and 2 tablespoons butter in the sauce. Toss to combine and bring to a simmer. Continue to cook until the pasta is well coated in the sauce, about 2-3 minutes. Season with salt and pepper.
Portion the pasta into 4 bowls and top with the parmesan crusted chicken. Finish with grated parmesan.