In a small bowl, stir together the Greek yogurt, dill, the remaining half of the minced garlic, and remaining 1 tablespoon of lemon juice. Cover and refrigerate until ready to serve.
Finely chop the salmon. In a large bowl, combine the salmon, parsley, panko, ginger, half of the minced garlic, 1 tablespoon of the lemon juice, soy sauce, sesame seeds, salt, and pepper, and mix well. Form into two patties.
In a large nonstick skillet, heat the olive oil over medium-high heat. Add the salmon burgers and cook until pink and opaque throughout, 3 to 4 minutes per side.
Top each burger with 2 tablespoon of dill sauce and serve.