Step 1
Toss 1½ lb. skinless, boneless rooster breasts, sliced on a diagonal ¼” thick, with 2 Tbsp. soy sauce and 1 Tbsp. mirin in a medium bowl. Sprinkle 1 Tbsp. cornstarch over; toss to coat.
Step 2
Pulse white and pale inexperienced components of 4 scallions, 6 garlic cloves, coarsely chopped, and one 2″ piece ginger, scrubbed, coarsely chopped, in a meals processor till very finely chopped.
Step 3
Warmth 2 Tbsp. vegetable oil in a big skillet over medium-high. Prepare rooster in skillet in a fair layer and cook dinner, undisturbed, till golden brown beneath, about 3 minutes. Flip rooster over and cook dinner till golden brown on different facet, about 2 minutes. Switch to a plate.
Step 4
Warmth remaining 2 Tbsp. vegetable oil in identical skillet. Add scallion combination and cook dinner, stirring, till aromatic, about 30 seconds. Add 8 oz. child bok choy, halved lengthwise, 8 oz. mushrooms, trimmed, sliced, and 8 oz. snow peas, trimmed, and cook dinner, tossing, till crisp-tender, about 2 minutes. Return rooster and any accrued juices to skillet. Add remaining 3 Tbsp. soy sauce and 1 Tbsp. mirin and ¼ cup water, scraping up any browned bits caught to backside of pan. Cook dinner, tossing, till greens are tender and sauce is barely thickened, about 2 minutes. Take away from warmth; style and season with kosher salt if wanted.
Step 5
Divide stir-fry amongst plates; prime with darkish inexperienced components of 4 scallions. Serve with cooked rice alongside.