Thaw the frozen shrimp by running cold water over a colander for about 5 minutes. Remove tails if they are any. Pat the shrimp dry with a paper towel and season with salt and pepper.
Heat 1 1/2 teaspoons of olive oil in a large skillet over medium-high heat. Cook half the shrimp for about 2-3 minutes per side, until lightly browned. Move to a plate. Repeat with another 1 1/2 teaspoons of oil and remainder of the shrimp.
Add 1 teaspoon of olive oil to the pan and cook the onion until tender, about 2-3 minutes. Add in the frozen mixed vegetables. Cook for another 4-5 minutes until the vegetables are tender and heated through. Add the balsamic vinegar and a sprinkle of salt and pepper. Stir for another minute until blended. Add shrimp and stir again until heated and well combined. Do not over cook shrimp!