In a medium bowl, whisk the egg, then add and mix the crab meat, breaking up large pieces.
Add mayonnaise, mustard, garlic, salt, thyme, cayenne, parsley, and almond flour. Mix well.
Portion out six ¼-cup scoops of the mixture and form into ½-inch-thick patties.
Place patties on wax paper-lined platter, cover with plastic wrap, and refrigerate for at least one hour.
Heat butter and olive oil in a large nonstick skillet over medium heat for 3 minutes. Add the crab cakes and cook for 4 minutes without moving until browned on the bottom.
Carefully flip the cakes, gently press to flatten slightly, and cook for another 3-4 minutes until browned. Serve on paper towel-lined plate.