In a medium bowl, whisk together the ricotta, Parmesan, eggs and yolks, ¼ cup of the water, and ½ teaspoon each salt and pepper. Set aside.
In a 7-quart Dutch oven over medium, cook the bacon until just crisp, 7 to 10 minutes. Use a slotted spoon to transfer to a paper towel-lined plate.
Pour off all but 2 tablespoons of fat from pot. Stir in the garlic and pepper flakes, then cook until fragrant, about 30 seconds. Stir the remaining 3¾ cups water and 1½ teaspoons salt and bring to a boil over medium-high. Stir in the pasta, reduce heat to medium and cook, covered and stirring occasionally, until al dente, 10 to 13 minutes.
Off heat, stir in the peas and reserved bacon. Let pasta sit for 5 minutes. Stir in the ricotta mixture, tossing to coat the pasta and form a creamy sauce. Taste and season with salt and pepper.
