In a small bowl, whisk together soy sauce, mirin, brown sugar, ginger, garlic, and sesame oil, set aside.
Heat 2 tbsp vegetable oil in a large skillet over medium high heat. Add broccoli and snap peas, and cook, 2-3 minutes, stirring just until the green color pops, and the broccoli and snap peas still have some crunch. Remove from pan and set aside.
Add 1 tbsp oil to the pan and add the shrimp in one layer and cook until pink, about 2 minutes each side.
Add in the soy sauce mixture and bring to a simmer. Add the broccoli and snap peas back in and coat them with the sauce.
Whisk the cornstarch and cold water together so there are no lumps. Add the cornstarch mixture, and cook until the sauce is thickened.
Serve over rice.
Garnish with sesame seeds and scallions