Heat oil in a hot wok and quickly stir-fry the capsicum and carrot until soft, about 2 minutes. Remove with a slotted spoon and set aside on a plate.
Add the garlic and ginger to the wok, stirring for 1 minute until aromatic. Add chicken and cook for 5 minutes until starting to brown. Stir in soy sauce, sugar, mirin, and chillies. Simmer on medium heat for 15-20 minutes until the liquid reduces.
Add the capsicum mixture back to the wok and toss for 1 minute until warm. Finish with a drizzle of sesame oil and a sprinkle of shallots. Serve alongside steamed rice.