In a saucepan, bring the rice and 2 cups water to a boil over medium-high heat. Lower the heat, cover and simmer until tender, 15 minutes. Turn off the heat.
Meanwhile, in a large nonstick skillet, cook the steak over medium-high heat, turning once, for about 8 minutes. Transfer to a cutting board and let rest.
Add the mirin to the skillet and bring to a boil; cook for 1 minute. Stir in the broth, soy sauce, ginger and sugar; cook for 2 minutes. Whisk in the cornstarch mixture and cook, stirring, until thickened, about 1 minute.
In a medium pot of boiling, salted water, cook the broccoli and squash until crisp-tender, about 3 minutes; drain.
Thinly slice the steak; add to the sauce to coat. Serve with the rice and vegetables.