Cook the udon noodles according to package directions; drain and set aside.
In a small bowl, whisk together the 1/2 cup low-sodium soy sauce, 1/4 cup rice vinegar, and 2 tablespoons hoisin sauce.
Heat a large skillet over medium-high heat and add the 2 tablespoons sesame oil.
If using the 1 pound ground chicken or turkey, add it to the skillet and cook, breaking it up, until browned, about 5 minutes. If not using meat, skip to the next step.
Add the sliced red/orange bell peppers, the grated 1-inch fresh ginger, and the seeded and chopped Fresno pepper to the skillet. Cook, stirring, until the peppers are tender-crisp, about 2–3 minutes.
Pour the soy sauce–vinegar–hoisin mixture into the skillet and add the chopped 1/3 cup fresh basil. Bring to a simmer and cook until the sauce reduces slightly and coats the meat and/or vegetables, about 3–5 minutes.
Add the cooked udon noodles to the skillet and toss until the noodles are evenly coated and heated through, about 1–2 minutes. Remove from heat.
Stir in the chopped 2 green onions and sprinkle the 2 tablespoons sesame seeds over the noodles. Serve immediately.