It doesn't take that much cream to make a creamy sauce with this one-pot method. But if you want even more richness, I won't stop you from adding another splash.
Crack the eggs into a medium bowl and add the cream and the Parmesan cheese; whisk to combine. Put the butter in a large pot over medium heat. When it melts, break the pasta into halves or thirds and add it to the pot; sprinkle with salt and pepper and stir to coat with the butter. Raise the heat a bit and cook, stirring constantly, until it's glossy and smells toasty, about a minute.2.
Begin to add water, 1/2 cup at a time, stirring after each addition. When the liquid is just about absorbed, add more. The noodles should be neither soupy nor dry. Keep the heat at medium to medium-high, stir frequently, and repeat as necessary.3.
Begin tasting the pasta 10 minutes after you added it; it should be tender but have some resistance when you bite. (It could take as long as 20 minutes to reach this stage.) When the pasta is ready, turn the heat to low and stir in egg mixture, adding a little more water if necessary to coat the noodles in sauce. Taste and adjust the seasoning. Serve right away, passing more Parmesan at the table.