Bring a large pot of water to boil, add the peas and boil gently until almost tender, about 2 minutes. Using a slotted spoon, or spider, remove the peas from the boiling water and rinse under cold water in order to cool completely.
To the same boiling water, add the pasta and cook according to package directions. While the pasta is cooking, make the pea sauce.
Place a skillet over medium heat, add the olive oil, garlic, shallot and red pepper flakes and cook for 2-3 minutes until fragrant. Add the butter and cook for about 1 minute more. Add the peas and stir to combine and season with salt and pepper. Remove from the heat and add the mint. Taste and season adjust salt and freshly ground black pepper as needed.
When the pasta is cooked, drain and add to the skillet with the peas. Stir together. Add the parmesan cheese, lemon juice and zest tossing gently to incorporate cheese. Break the burrata up into small pieces and dot the top of the skillet with it and garnish with extra mint leaves and pea tendrils. Serve immediately.