Heat an 8-in. nonstick omelette or fry pan over medium heat. Add 1 Tbsp. olive oil and coat pan. Add in the red pepper, onion, garlic and sauté until soft and golden. Cool mixture and set aside.
In a large bowl, whisk together mayonnaise, egg yolk, mustard, lemon zest, lemon juice, capers and cayenne pepper.
Add in the cooled red pepper mix and crab meat and continue to mix until completely incorporated.
Add 1/4 c. to 1/2 c. breadcrumbs or until the crab cake mixture can be shaped into a ball. The mixture should not be too dry or else the cakes fall apart during searing. Season the crab mixture to taste.
Form rounded 1 Tbsp. balls of crab mixture. Gently flatten into 1-in. rounds. Coat with remaining breadcrumbs and transfer to a shallow tray.
Chill crab cakes at least 30 minutes and up to 4 hours.
Heat a nonstick double griddle pan over medium heat. Add butter and remaining olive oil to coat pan.
Working in batches, fry crab cakes until golden brown on both sides. Do not crowd the pan.
Transfer browned crab cakes to a parchment lined baking sheet. Warm crab cakes in 300°F/150°C oven while other batches fry and serve.