Add a steamer basket to a small pot filled with about 1” (2.5cm) of water. Bring the water to a boil, then add the carrots to the steamer basket, cover and steam until very tender, about 10 minutes.

Add the steamed carrots, shrimp, green onions, egg, panko, garlic powder and ginger to the bowl of a food processor fitted with the blade attachment. Blend until the mixture is ground.

Heat a nonstick skillet over medium-low heat, add the oil and heat through. Drop the patties into the pan in rounded spoonfuls. Cook the patties until golden brown, about 2 minutes, then use a spatula to flip them. Continue to cook until cooked through, about an additional 2 minutes.

Remove from the pan, then let cool and serve or store. Store refrigerated for up to 1 week or frozen in resealable plastic bags for up to 3 months.