In a medium saucepan, bring the water and a pinch of salt to a boil. Add the rice, reduce to a simmer, cover, and cook until tender, 15 to 20 minutes. (see How to salvage not-so-perfect rice)
Meanwhile, in a small saucepan, cook the peas in a little water until tender.
Crack the egg or eggs into a small bowl, season with salt and pepper, and beat until frothy. When the rice is done and all the water is gone (drain off any excess and return the rice to the pot, if necessary), rapidly stir in the beaten egg, butter, and cheese. Add the peas, scallions, basil or chervil, and lemon zest; stir to combine. Season with salt and pepper. Serve with additional grated cheese.