Place the drained salmon in a large bowl. Flake it well with a fork into tiny pieces.
Add the eggs, Dijon mustard, garlic, kosher salt, black pepper, and thyme. Mix well. Mix in the chopped parsley.
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.
Mix the remaining ingredients together to make your salsa and serve it over the salmon cakes.