Bring 4 quarts water to boil in large pot over high heat. Add 12 ounces fresh lo mein noodles or 8 ounces spaghetti and cook, stirring occasionally, until just tender, 3 to 4 minutes for lo mein and 7 to 12 minutes for spaghetti. Drain noodles and rinse under cold running water. Drain well and set aside.
Heat 2 teaspoons toasted sesame oil, 2 teaspoons vegetable oil, 8 minced garlic cloves, and 2 teaspoons grated ginger in 12-inch nonstick skillet over medium-low heat and cook, stirring occasionally, until beginning to turn golden brown, about 4 minutes.
Add 1 pound chicken thighs, trimmed, sliced crosswise ½ inch thick; 6 tablespoons soy sauce; 6 tablespoons rice wine; and 2 tablespoons packed brown sugar. Increase heat to medium-high and bring to simmer. Cook, stirring occasionally, until chicken is cooked through and sauce is reduced and begins to cling to chicken, about 6 minutes.
Add 2 heads baby bok choy, sliced on bias ¼ inch thick and 1–2 Fresno chiles, halved, seeded, and sliced thin crosswise and cook until bok choy is just beginning to soften, about 1 minute. Add noodles and toss to combine. Off heat, stir in 1 cup Thai basil leaves and remaining 1 teaspoon sesame oil. Garnish with extra basil and serve.
