Heat olive oil in a pan over medium-high heat. Add onion and soy sauce; cook until tender, about 5 minutes. Stir in garlic; cook until fragrant, about 1 minute. Add turkey and cook, breaking into smaller pieces, until no longer pink, about 5 minutes.

Make the sauce by whisking soy sauce, rice vinegar, brown sugar, sesame oil, red pepper flakes, and ginger together in a small bowl. Pour over turkey mixture and simmer until slightly reduced, 2 to 3 minutes.