Bring water and brown rice to a boil in a saucepan; cook until rice has softened, 15 to 20 minutes. Drain.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add green beans, cover, and steam until tender, 2 to 6 minutes.
Heat olive oil in a large skillet over medium-high heat. Saute green beans and rice in hot oil until lightly crisped, 5 to 10 minutes. Stir in feta cheese; drizzle olive oil over the top and season with black pepper.