Chop the veggies: Chop the broccoli. Thinly slice the bell peppers. Remove the stems of the shiitake mushrooms and slice (or if using baby shiitakes, you can leave the stems on).
Make the stir fry sauce: Whisk together all ingredients until a smooth sauce forms.
Cook the vegetables: In a large skillet, heat 2 tablespoons oil over medium high heat. Add the broccoli or broccolini, bell pepper and mushrooms. Add 2 pinches kosher salt and cook 5 to 6 minutes, stirring occasionally, until crisp tender. Remove the vegetables to bowl.
Cook the shrimp: Add the additional 1 tablespoon sesame oil to the pan. Add the shrimp, green onions and ginger (optional). Cook for 1 to 2 minutes until the shrimp are almost opaque, turning once. Then add back the vegetables and the sauce. Reduce the heat to low and cook until the sauce is thickened.