Heat a large skillet or wok over medium-high heat.
Add 1 tablespoon of oil to the skillet, swirling to coat the surface.
Add the shrimp to the skillet in a single layer.
Cook the shrimp for 2-3 minutes until they turn pink and opaque, then remove from the skillet.
In the same skillet, add a little more oil if necessary, then toss in the onions and garlic.
Add the bell peppers and broccoli, stir frying for about 4-5 minutes.
Stir in the grated ginger and cooked shrimp, continuing to stir-fry for another 2 minutes.
Pour in the soy sauce and sesame oil, tossing to coat all ingredients evenly.
Taste and adjust seasoning with salt and pepper as needed before serving.