In your wok or large skillet, heat the vegetable oil over medium-high heat. You want the oil to shimmer but not smoke.
Add the shrimp to the pan in a single layer. Allow them to cook for about 2-3 minutes on one side until they turn pink and opaque. Flip them over and cook for an additional 1-2 minutes. Once done, remove the shrimp from the pan and set them aside.
In the same pan, add the broccoli florets, red bell pepper, and julienned carrot. Stir-fry for about 4-5 minutes until the vegetables are tender-crisp.
Add the minced garlic and ginger to the pan. Stir for about 30 seconds until fragrant, making sure not to burn them.
In a small bowl, whisk together the low-sodium soy sauce, cornstarch, and water until smooth. Pour this mixture over the sautéed vegetables and stir well to combine. Allow the sauce to thicken for about 2 minutes.
Return the cooked shrimp to the pan, and add the sesame oil. Toss everything together to make sure the shrimp and vegetables are well-coated with the sauce. Cook for an additional minute to heat through.
Serve your shrimp stir-fry hot over a bed of cooked rice. Enjoy the burst of flavors and the delightful crunch of fresh vegetables!