Toast the orzo. Heat the oil in a wide skillet over medium-high heat. Add the orzo and toast, stirring constantly, until it smells nutty and turns a shade darker, about 90 seconds. The pan will look dry, and that is fine; just keep it moving.
Simmer like a lazy risotto. Pour in the broth and water. Stir, then hold at a strong simmer, stirring every minute or so, for about 7 minutes. The orzo drinks the liquid and releases its starch, and that starch is the whole sauce. Keep a little extra water at your elbow.
Add the peas and chicken. When the orzo is just shy of al dente and the liquid has gone saucy, stir in the frozen peas and shredded chicken. The pan will cool down, so bring it back to a simmer for 2 minutes, until the peas are bright green and everything is hot through.
Finish off the heat. Pull the pan off the heat. Add the Parmesan in two handfuls, stirring hard between each so it emulsifies instead of clumping. Then stir in the lemon zest, lemon juice, black pepper, and chili flakes. Salt to taste.
Serve. Loosen with a splash of water if it has tightened up. Serve right away, with more Parmesan grated over the top.