Heat wok over high heat. Swirl in the oil and add the chicken. Adjust the heat between medium and medium-high as the chicken browns. Do not cook chicken all the way through. Remove to a plate, leaving the pan drippings.
Add shallots and cook until just softened. Add the curry paste or powder and cook, stirring, 30 seconds or until fragrant (with powder, pan may begin to smoke). Return chicken to wok. Add coconut milk and broth and bring to a boil over high heat, uncovered. Add bell pepper, carrot, salt and pepper. Cover, reduce heat to medium-low, and simmer 15-30 minutes.
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