In a medium bowl, gently whisk together the eggs, breadcrumbs, green onions, parsley, mayonnaise, minced garlic, lemon juice, Old Bay seasoning, salt, and pepper.
Stir in the shredded cheddar cheese until everything is combined.
Carefully add the lump crab meat to the bowl. Fold it in GENTLY using a spatula, trying not to break up the crab lumps too much.
Divide the mixture into 4-6 equal portions (depending on desired size). Gently form each portion into a patty, about 1 to 1.5 inches thick. Do not pack them too tightly.
If the patties feel loose, pop them in the fridge for 10-15 minutes to firm up.
Heat a tablespoon or two of oil (like vegetable or canola oil) in a large non-stick skillet over medium-high heat.
Carefully place the crab cakes in the hot skillet (cook in batches if needed to avoid overcrowding).
Cook for about 4-6 minutes per side, until golden brown and heated through.
While the crab cakes are finishing or in between batches, melt the butter in a small saucepan or microwave-safe bowl.
Stir in the lemon juice and garlic powder. Whisk briefly.
Plate the hot crab cakes and generously drizzle the warm lemon butter sauce right over the top.
Serve immediately!