Bring a large pot of water to a boil. Season with salt and add the beet and pasta. Cook, stirring occasionally with a wooden spoon, until the pasta is al dente. Drain, reserving 1 cup of the pink pasta cooking water. Discard the beet or save for another use.
Meanwhile, place a large Dutch oven over medium heat. Add the oil, bacon, onion, garlic and red pepper flakes. Season with salt and cook, stirring occasionally with a wooden spoon, until the bacon is cooked through and the onion is translucent, 7 to 8 minutes.
Pour the tomatoes into a medium bowl and crush them with your hands. Pour the tomatoes and juices into the Dutch oven. Stir in the lemon zest and juice, then stir in the peas and heavy cream. Season with salt to taste.
Stir in the drained pasta and reserved pasta water. Stir in 3/4 cup of the Parmesan. Serve immediately, garnished with the remaining Parmesan.
The beet in this recipe acts as a fun natural dye that gives the noodles extra color, but the dish is just as delicious without the beet.