Place the crab in a medium mixing bowl. If there are large lumps of crab, flake them with a fork a bit, so the crab cakes will hold together better.
If using rolled oats instead of quick oats, measure out ½ cup and pulse them in a food processor or blender to make them more fine. Add the oats to the bowl of crab.
Peel a medium shallot and finely chop it. (It should equal about ⅓ cup of chopped shallot.) Melt the butter in a 12-inch skillet over medium heat and cook the shallots in it until they are soft. Add the buttery shallots to the crab bowl.
Beat an egg in a small bowl or measuring cup and whisk in the mayonnaise. Add the egg mixture to the bowl with the crab. Add the Old Bay, pepper and salt and gently fold the crab cake mixture with a silicone spatula to combine. Cover the bowl and refrigerate the mixture for at least an hour (or up to one day) so the crab cakes you make will hold together better.
To shape the crab cakes, use a ½-cup measuring cup to scoop each one. Place the mound of batter between your hands and gently squeeze it into a patty. You should end up with seven crab patties.
Wipe out any bits of shallot left in your skillet with a paper towel, so they don't burn during frying. Add three tablespoons of oil to the skillet. Heat it on medium high until hot. Use a narrow metal spatula to carefully add the crab cakes to the pan in a single layer, without any of them touching.
Cook the crab cakes on the first side until a brown crust develops on the bottom, and the crab cakes are easy to nudge. It could take 5-6 minutes. (If you try flipping them too soon, they'll break.) If the oil splashes, lower the heat slightly, so it's just higher than medium. If you have a frying shield, it helps to place it over the pan to prevent oil splashing out.
When you can easily nudge the crab cakes and they slide, flip them over carefully using a narrow spatula. Cook the second side for about five minutes, until the bottom is browned and crispy. Transfer the cooked crab cakes to a plate lined with paper towels to absorb the oil. Let them rest for five minutes.
To serve, squeeze on some lemon juice and serve with lemon wedges. You also could serve the crab cakes with mayo, if desired.
Store leftovers covered in the refrigerator for up to four days.
Note that lump crab meat is gluten-free, while imitation crab meat contains wheat and is not gluten-free. Refrigerated lump crab meat is the best kind to use for crab cakes, due to its quality and convenience. If you need the crab cakes to be gluten-free, you must use gluten-free oats. While oats are naturally gluten-free, during the manufacturing process they may come in contact with wheat products. Always check the label first.If you don't need to make gluten-free crab cakes, feel free to use regular oats or even bread crumbs.Pan-frying crab cakes in oil will give them a nice, crispy texture on the outside, and a tender texture inside. After testing other methods, I can say frying makes the best crab cakes. Air Fryer Crab CakesAir fryer crab cakes are the next best thing to pan-fried. Spray the tops of the crab cakes with cooking spray, then air fry them at 400 degrees F for 12 minutes total. You'll need to flip them over after the first six minutes and spray the other sides with oil before continuing to cook them.Baked Crab CakesBaking crab cakes will not provide the same crispy results as pan-frying them on the stove. But if you wish to make crab cakes in the oven, you can bake them on a greased sheet pan at 450 degrees F for 12-14 minutes without flipping them. Then, broil them on the top rack of your oven for three minutes.