Make the pesto: Bring a small saucepan of lightly salted water to a boil. Add peas and cook for 2 minutes (they should be tender to the bite but retain a bit of structure). Drain peas and let them cool down for a few minutes.
Make the rice: bring a big pot of water to a boil, dump in rinsed brown rice and boil, uncovered, for 30 minutes. Reserve 1 cup cooking water for the pesto as you drain the rice. Return the rice to the pot and cover. Let the rice steam in the pot for 10 minutes.