Begin by browning the chicken in a large skillet over medium heat. Remove the chicken and set aside. In the same skillet, sauté the onion, carrots, and potatoes until softened. Add the peas, green bell pepper, and red bell pepper and cook for a few minutes more.
In a separate bowl, whisk together the flour, curry powder, cumin, coriander, turmeric, and cayenne pepper (if using). Gradually add the chicken broth, whisking constantly to prevent lumps. Pour the mixture into the skillet with the vegetables and bring to a boil. Reduce heat and simmer for 15 minutes, or until the vegetables are tender.
Return the chicken to the skillet and stir in the heavy cream, soy sauce, honey, and sesame oil. Simmer for an additional 5 minutes, or until the sauce has thickened.
To serve, spoon the curry rice over a bed of cooked rice. Garnish with chopped green onions or cilantro for an extra burst of flavor.