Hambagu (Japanese-Style Hamburger with Tangy Sauce)

Ingredients

• 1/2 cup Japanese soy sauce
• 1/2 cup sweet rice wine mirin
• 1/2 cup rice wine sake Japanese
• 1/2 cup granulated sugar
• 1/4 cup yellow onion roughly chopped
• 5 ginger thin round slices peeled
• 2 garlic cloves medium, smashed and peeled
• 1 tablespoon unsalted butter
• 1 medium yellow onion very finely diced
• 1/2 cup panko breadcrumbs
• 1/4 cup whole milk
• 1 pound ground beef preferably 80% lean
• 1 teaspoon kosher salt
• 1/2 teaspoon freshly grated nutmeg
• white pepper to taste
• 1 large egg
• 1 tablespoon vegetable oil plus extra for your hands
• 1 cup teriyaki sauce
• 1/4 cup ketchup
• 2 teaspoons Dijon mustard