Heat olive oil in a large wok or skillet over medium heat. Add shrimp, season with salt and black pepper, and cook for 2–3 minutes until pink. Remove shrimp and set aside.
In the same skillet, heat sesame oil over medium heat. Add broccoli, bell pepper, and snap peas. Stir-fry for about 7 minutes until vegetables are slightly tender. Add a splash of water if they start to brown too quickly.
Stir in the garlic and ginger and cook for about 1 minute until fragrant.
In a small bowl, whisk soy sauce, lime juice, brown sugar, cornstarch, and red pepper flakes.
Pour the sauce into the skillet and toss the vegetables to coat.
Return the shrimp to the pan and cook for about 2 minutes, stirring frequently, until everything is heated through.
Serve this delicious Shrimp Stir Fry immediately over rice or noodles.