Drain the salmon cans thoroughly. Place the salmon in a large bowl. Flake it well with a fork into tiny pieces.
Add the eggs, mayonnaise, Dijon mustard, garlic, kosher salt, black pepper, and thyme. Mix well.
Mix in the chopped parsley.
Heat the olive oil over medium heat in a large nonstick skillet, about 3 minutes.
Using an ice cream scoop, transfer four mounds of the mixture to the skillet. Pack the mixture into the scoop, then release into the skillet and gently flatten.
Cook until well-browned and crispy, about 3 minutes on each side. Place in the oven to keep warm while you cook the second batch.
To ensure that the cakes don’t fall apart, drain the salmon REALLY well and flake it well, use large eggs, and mix the ingredients thoroughly.About half the olive oil will remain in the skillet, and the nutrition info reflects that. But you need all of it to properly fry the cakes.