Peel the garlic and slice each clove paper-thin; set aside.
Bring a large pot of water to a boil, salt generously, and cook the squid ink pasta according to package directions; reserve 1 cup of pasta cooking water, then drain.
Heat a large frying pan over medium-high heat, add the olive oil, then add the shrimp and cook about 1 minute per side until pink and just opaque; remove if desired or leave in pan.
Reduce heat to medium, add the cubed butter, sliced garlic, dried oregano, and chili flakes to the pan; as the butter melts, pour in 1/4 cup of the reserved pasta water and simmer gently for 2 minutes to form a sauce. Season with salt and pepper to taste.
Add the arugula or baby spinach to the sauce and cook until just wilted, about 30–60 seconds.
Add the drained pasta to the pan and toss to combine, adding more reserved pasta water as needed to loosen the sauce; heat through for 30–60 seconds.
Serve immediately, topped with grated parmesan if desired.