Combine the crab meat, potatoes, cheese, bread crumbs, bell pepper, egg, mustard, dill, salt, and pepper in a large bowl and mix until well blended.
Heat half the oil in a large nonstick skillet over medium-high heat.
Shape the mixture into twelve patties. Add half the patties to the skillet and cook until golden brown, about five minutes. Flip the patties and cook an additional 4 to 5 minutes.
Repeat with the remaining oil and patties.
Tip: If you think your children may be averse to the tiny bits of red bell pepper, use a yellow or orange pepper instead so it blends right in.