In a medium bowl, lightly whisk the egg with a fork. Add the crab meat. 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 almond flour.
Use a 4-tablespoon scoop to portion out six portions of the mixture. Use your hands to form the portions into six ½-inch-thick patties.
Place the patties on a platter lined with wax paper. Cover them loosely with plastic wrap and refrigerate them for at least one hour.
Heat the butter and olive oil in a large (12-inch) nonstick skillet over medium heat for about 3 minutes. Add the crab cakes. Cook them for about 4 minutes without moving, until you can tell by their edges that the bottoms are browned.
Carefully flip the cakes using two spatulas. Very gently press on their tops to slightly flatten them, then cook them on the other side until browned, about 3-4 more minutes.
Remove them to a plate lined with paper towels, then serve them.
Video
Notes
The fresher the crabmeat, the better the cakes will taste.
If out of fresh garlic, use 1 teaspoon of garlic powder.
It's important to chill the patties for at least an hour before frying them. They are quite delicate and could easily fall apart when you fry them if they're not chilled first.
At least half the cooking fat will remain in the skillet, but it's needed for properly cooking the patties. The nutrition info reflects this.
If you don't have a skillet large enough to accommodate all patties, fry them in two batches, and keep the first batch in an oven set to the "keep warm" setting.
You can keep the leftovers in the fridge, in an airtight container, for up to three days. Reheat them in a 350°F oven to retain their crispness. They are also very good cold, straight out of the fridge!
Once they're completely cool, you can place the cakes in freezer bags and freeze them for up to three months. If you stack them, separate them with wax paper squares. Thaw them overnight in the fridge before reheating them.