In a small saucepan, combine soy sauce, brown sugar or honey, garlic, ginger, rice vinegar, and sesame oil. Bring to a simmer.,Stir in cornstarch slurry and cook until sauce thickens. Remove from heat and set aside.,In a large skillet, heat oil over medium-high heat. Add sliced chicken and cook until golden and cooked through.,Pour teriyaki sauce over the chicken and stir to coat. Simmer for 2–3 minutes to absorb flavor.,To assemble wraps, lay out tortillas and layer with lettuce or cabbage, carrots, cucumbers, rice (if using), and teriyaki chicken.,Top with green onions, cilantro, and sesame seeds. Roll up tightly and slice in half if desired. Serve warm or at room temperature.