Cook the pasta in a large pot of boiling salted water until al dente. Reserve 1/2 cup of the starchy pasta water before draining.
Season the chicken (or shrimp) with salt, black pepper, and a pinch of red pepper flakes. Heat 1 tbsp olive oil in a pan over medium-high heat.
If using chicken, sear for about 5-6 minutes per side until golden brown and cooked through. Remove from the pan and let it rest before slicing.
If using shrimp, cook for 1-2 minutes per side until pink and opaque. Remove from the pan and set aside.
In the same pan, reduce heat to medium, add butter, the remaining olive oil, garlic, and red pepper flakes. Let them sizzle for a a few seconds to a minute until fragrant, not burnt.
Toss in the pasta, lemon zest, and juice. Stir well, adding the reserved pasta water a little at a time until the sauce coats everything beautifully.
Slice the chicken and add it (or toss in the shrimp). Mix everything together with fresh parsley and Parmesan.
Serve immediately. Extra cheese on top? Always. Maybe a drizzle of chili oil if you’re feeling bold.