Bring a large pot of salted water to a boil. Add the squid ink pasta and cook according to package instructions until al dente. Reserve 1 cup of pasta water before draining. Drain and keep aside.
In a large skillet melt butter over medium heat. Add the shrimp, season with salt and black pepper. Saute for 1-2 minutes on each side, then transfer to a plate.
Put the tomatoes in the same skillet. Season with salt and red chili flakes. Cook until the tomatoes start to pop, about 3-4 minutes. Add the garlic and cook until fragrant, about 40-50 seconds.
Reduce the heat to low, add 1/4 cup of reserved pasta water, honey , lemon juice and zest. Season with salt and pepper. Bring to a simmer and cook for 5-7 minutes or until the sauce thicken slightly.
Add the cooked pasta and shrimp. Mix well. If needed , add more pasta water to thin the sauce.
Divide the pasta between the bowls and top with burrata and shaved parmesan cheese. Enjoy!