Start by defrosting the shrimp in a bowl of warm (not hot) water for 10 minutes.
Remove the shells and devein the shrimp. To devein it, grasp the shrimp on both sides of its body and gently squeeze. Make a shallow cut down the length of the shrimp's back, then lift out the vein with the tip of a knife. Alternatively, you can buy pre-shelled and deveined shrimp.
Gently pulse the shrimp in a food processor until coarsely chopped, but not pureed. Alternatively, you can finely chop them with a knife.
In a large bowl, combine the shrimp with the panko bread crumbs, eggs, green onions, lemon juice & zest, mayo, paprika, onion powder, and black pepper. Mix well.
Divide the mixture into 8 portions and form each into a patty.
Heat the olive oil in a shallow pan, over medium-high heat. Cook the shrimp patties for approximately 4 minutes on each side or until they are cooked through. You will likely have to do this in batches. If the shrimp cakes are browning too quickly on the outside, lower the temperature to ensure they cook through evenly.
For the broccoli, fill a large pot halfway with water and bring it to a boil.
Wash the broccoli and cut into florets (leave a good amount of stem on each floret).
Place the broccoli in a steamer basket on top of the pot of water. Cover and steam for 10-15 minutes, or until fork tender.