In a large pot, start heating water to boil pasta.
In a pan, heat olive oil over medium heat and fry prosciutto, turning frequently, until golden brown and crispy. Set aside on a paper towel lined plate to drain.
Add butter to pan and sauté garlic and crushed red pepper for about 2 minutes. Add tomato paste and sauté for another 2 minutes. Add 1/2 cup of vodka and let simmer until reduced by half.
Add tomatoes, heavy cream, salt and pepper and bring to a simmer. Reduce heat to medium low and let simmer for about 10 minutes, stirring occasionally. Stir in 1 tablespoon vodka to finish sauce.
While pasta sauce is simmering, cook pasta according to package instructions. Salt pasta cooking water with 1 1/2 tablespoons kosher salt. Reserve 1/2 cup of pasta water to thin tomato sauce, only if needed, to desired consistency. Drain pasta and add to sauce.
Top pasta with burrata. Drizzle burrata with olive oil and top with additional salt and pepper. Break up prosciutto and sprinkle crispy prosciutto over burrata and vodka sauce pasta. Finish with fresh basil and parmesan.