In a medium bowl, lightly whisk the egg with a fork. Mix in the crabmeat. Mix well with a fork, pressing on the crab meat with the fork and breaking up any large pieces.
Mix in the mayonnaise, mustard, garlic, kosher salt, thyme, and cayenne pepper. Then Mix in the parsley and the almond flour.
Use a 1/4-cup scoop to portion out six portions of the mixture. Use your hands to form the portions into six 1/2-inch-thick patties.
Place the crab cakes on a platter lined with wax paper. Cover loosely with plastic wrap and refrigerate for at least one hour.
Heat the butter and olive oil in a large nonstick skillet over medium heat, about 3 minutes. Add the crab cakes. Cook them for about 4 minutes without moving, until you can see on the edges that the bottoms are browned.
Carefully, using two spatulas, flip the crab cakes. Very gently press on their tops to slightly flatten, then cook on the other side until browned, about 3-4 more minutes. Remove them to a plate lined with paper towels, then serve.
