In a large skillet over medium heat, add 1 Tbsp oil and sautee diced bell pepper and onion until golden and soft (7-9 min) then remove from heat and let cool.
In a large mixing bowl, whisk together 2 eggs, 3 Tbsp mayo. Drain and pick over the crab meat to make sure there aren’t any stray shells, lightly breaking up big pieces of meat. Transfer to the large bowl with egg mixture.
Add cooled bell pepper and onion, panko crumbs and parsley and stir until combined and moistened. Cover and refrigerate 30 minutes.
Divide mixture into about 15 cakes. With wet hands, lightly shape into 1/2 thick patties. Place a large non-stick pan over medium heat with 1 Tbsp oil and 1 Tbsp butter and sautee crab cakes in batches for 4-5 minutes per side (reduce heat if browning too quickly). Transfer to a serving platter and repeat with remaining crab cakes adding more oil and butter.