Peel the garlic and slice each clove very thinly; set aside.
Bring a large pot of water to a boil, salt generously, and cook the squid ink pasta according to package instructions; reserve 1 cup of the pasta cooking water before draining.
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 cooked through; remove any excess juices if necessary.
Reduce heat to medium. Add the butter cubes, sliced garlic, dried oregano, and chili flakes to the pan; the butter should melt quickly.
Pour in 1/4 cup of the reserved pasta water and simmer gently for about 2 minutes to form a sauce; season generously with salt and pepper.
Add the arugula or baby spinach to the sauce and toss until wilted.
Drain the pasta and add it to the pan with the butter-shrimp sauce; toss to combine, adding more reserved pasta water as needed to loosen the sauce.
Serve immediately, topped with grated parmesan if desired.