Fry the patties without moving them until the bottoms are deep golden brown and the edges look set, about 3 to 4 minutes. Carefully flip each patty and cook the second side until golden and the shrimp are opaque in the center, another 3 to 4 minutes.
Transfer the cooked shrimp patties to a paper towel–lined plate or a wire rack set over a baking sheet to drain briefly. Repeat with the remaining mixture, adding a touch more oil to the pan as needed and letting it reheat before adding more patties.
Serve the shrimp patties right away while they’re hot and crisp, garnished with extra sliced green onion if you like, and accompanied by lemon wedges and your favorite simple dipping sauce.
For a slightly richer texture, you can replace 2 tablespoons of the chopped shrimp with 2 tablespoons of full-fat mayonnaise, folding it in with the shrimp; just be aware the mixture will be softer and you may want a bit more almond flour. If you prefer a different low-carb binder, finely ground pork rinds can stand in for the almond flour at the same volume, giving a slightly more intense savory flavor and extra crunch. Swap the green onion for finely chopped fresh chives or flat-leaf parsley for a milder herbal note, or add a pinch of smoked paprika or cayenne to the egg mixture for a gentle warmth that doesn’t overwhelm the shrimp. To bake instead of pan-fry, lightly oil a parchment-lined baking sheet, spoon and flatten the patties, mist the tops with a little oil, and bake at 400°F (200°C) for 10 to 12 minutes, flipping once, until golden; they won’t be quite as deeply crisp as the skillet version, but the texture will still be pleasantly firm and low in carbs.