Combine water and mushrooms in a large saucepan; bring to a boil. Cover, reduce heat, and simmer 2 minutes. Remove from heat; let stand 30 minutes. Drain mushrooms, reserving 1 cup liquid. Coarsely chop mushrooms.
Wash Brussels sprouts thoroughly, and remove discolored leaves. Trim stem ends, and cut in half; set aside.
Combine chicken broth and 1 cup reserved liquid in same saucepan; bring to a boil. Add rice and mushrooms. Cover and simmer 50 minutes. Remove from heat; drain.
Melt 2 tablespoons butter in a large nonstick skillet over medium-high heat; add leeks. Sauté 3 minutes or until tender. Remove from skillet; set aside. Melt remaining butter in skillet over medium-high heat; add Brussels sprouts, and sauté 5 minutes or until browned. Add 3 tablespoons water; cover and cook 5 to 6 minutes or until Brussels sprouts are fork-tender, adding more water as necessary.
Add cooked rice, leeks, salt, and pepper; stir gently. Cook over medium-low heat just until thoroughly heated.