Separate the broccoli into small florets, place them in a deep bowl filled with water, and let soak for 5 minutes to rinse them thoroughly.
Cut the carrot into chunks.
Pour water into a saucepan and bring it to a boil. Add the broccoli and carrot, cook for 2 minutes, then remove from the heat and drain well.
Transfer the vegetables to a blender or food processor and pulse until finely chopped. Add the chopped shrimp, eggs, flour, and cornstarch, then mix well until you get a thick batter.
Heat a thin layer of vegetable oil in a non-stick pan. Spoon the vegetable batter into the pan to form small patties and cook on both sides until golden and slightly crispy.
Notes
Use fresh, firm broccoli for the best color and flavor in the patties.
Do not skip draining the vegetables well after blanching to avoid a watery batter.
Chop the shrimp finely so every bite has an even mix of seafood and veggies.
Adjust the salt depending on how salty your shrimp is.
Fry the patties over medium heat so they cook through without burning.
Serve with a light dipping sauce to balance the sweetness of the vegetables.