In a medium bowl, whisk together the coconut milk, peanut butter, chili garlic sauce, Worcestershire sauce, lime juice, brown sugar, coriander, and cumin. Set aside.
In a large nonstick skillet, warm 2 tablespoons vegetable oil over medium-high heat. Once oil is shimmering, season the chicken with salt and pepper and add to the skillet. Cook, undisturbed for 1 minute to develop a crust. Then saute for 4 minutes. Transfer to a plate and keep warm.
Add the remaining vegetable oil to the skillet; toss in the broccoli and carrots. Saute for about 3 minutes until vegetables are tender.
Add the cooked chicken back to the skillet, along with any accumulated juices, and the ginger. Cook for about 30 seconds until fragrant.
Give the sauce a stir and pour it into the skillet. Toss to coat only for 15-20 seconds to warm through. Remove from heat.
Serve immediately with cooked white rice and a sprinkle of chopped Thai basil.
