Place vegetable oil, vinegar, soy sauce, sugar, hoisin sauce, sesame seeds, sesame oil, Dijon mustard, ginger, shallot, garlic and pepper in a blender or food processor and blend until smooth. (Or, grate the ginger and mince the shallot and garlic then whisk all ingredients together.) Refrigerate in a covered container.
Hull and slice or quarter strawberries. Combine strawberries, chicken, greens, fennel and green onion in a large bowl. Drizzle with dressing and toss gently until evenly mixed.