Begin by spreading the lump crab meat on a baking sheet lined with parchment paper and broiling it for 3 minutes.
Remove the baking sheet from the oven and transfer the crab meat to a large bowl.
In a saucepan, saute the chopped red onion, celery and red pepper in 1 teaspoon of extra virgin olive oil for 5 minutes.
Remove the saucepan from the heat and allow the vegetable mixture to cool.
Add the cooled vegetable mixture and the julienned basil to the crab meet and mix.
Fold in the mayonnaise and the cracked black pepper.
Use an ice cream scoop to scoop the mixture into mounds. Arrange the crab cake mounds onto a baking sheet lined with parchment paper.
Bake the crab cakes at 350ºF for 12 minutes, then turn on the broiler and broil the crab cakes for 3 minutes.
Remove the crab cakes and plate them on top of the Cajun Lobster Sauce (recipe below) and serve with lemon wedges.