Start by seasoning the chicken breasts with salt and pepper. In a large skillet, heat 2 tablespoons of olive oil over medium-high heat. Add the chicken and cook for about 6-7 minutes on each side, or until cooked through and golden brown. Remove from the skillet and let it rest before slicing it into thin strips.
In a large pot of boiling water, cook the brown rice noodles according to package instructions until al dente. Drain and rinse them under cold water to stop the cooking process. Set aside.
In the same skillet used for the chicken, add the remaining olive oil. Toss in the minced garlic and sauté for about 30 seconds until fragrant. Then, add the sweet chili sauce, brown sugar, soy sauce, and rice vinegar. Stir well to combine and let the sauce simmer for a couple of minutes.
Add the sliced bok choy and green onions to the skillet, stirring to coat them in the sauce. Cook for about 3-4 minutes until the bok choy is tender yet still crisp.
Return the sliced chicken to the skillet along with the cooked noodles. Pour in the light coconut milk, tossing everything together until well mixed and heated through. Adjust seasoning if needed.
Remove from heat and stir in the freshly torn cilantro, chopped peanuts, and Thai basil. Drizzle with toasted sesame oil for added flavor. Serve the Thai-Style Chicken Street Noodles hot, garnished with extra peanuts, cilantro, and lime wedges on the side for squeezing over the top.