In a large mixing bowl, whisk together the egg, mayonnaise, Dijon mustard, Worcestershire sauce, Old Bay seasoning, lemon juice, lemon zest, parsley, black pepper, optional salt, and optional hot sauce until well combined.
Add the crab meat and cracker crumbs. Gently fold the mixture together, being careful not to break up the large pieces of crab.
If the mixture seems too wet to hold its shape, add an additional tablespoon of cracker crumbs.
Divide the mixture into 6 equal portions and shape into thick crab cakes about 1 inch tall.
Place the crab cakes on a parchment-lined baking sheet and refrigerate for 1 hour.
Remove the crab cakes from the refrigerator and let them sit at room temperature for 10 minutes.
Heat the butter and oil in a large skillet over medium heat.
Cook the crab cakes for 4 to 5 minutes per side, or until deeply golden brown and heated through.
To make the aioli, whisk together the mayonnaise, lemon juice, lemon zest, and garlic until smooth.
Serve immediately with lemon wedges and lemon aioli, if desired.