Start the white rice on the stove or in a rice cooker.
Pat chicken with paper towel to remove any moisture. Season with kosher salt and black pepper. Heat oil in a heavy bottomed pot. Brown the chicken in batches, skin side down first.
Add the diced onion and butter to the pot. Sauté until translucent, about 7-8 minutes.
Add the garlic and ginger and mix all together. Sauté about 1 minute more.
Add 1 piece Japanese curry roux, 1 Tbsp curry powder, and 1 tsp garam masala. Stir to coat the onion mixture in the spices. Add 1 Tbsp tomato paste and sauté until fragrant.
Gradually add half the chicken broth, scraping the brown bits on the bottom of the pot. Add the honey and stir to incorporate it. Transfer the chicken back to the pot.
Add the carrots and the rest of the chicken broth. (We added some leftover chicken gravy. You can also add mushrooms at this point.)
Bring to a boil, reduce to a simmer. Simmer for approx 30-40 min, until the chicken is cooked all the way through and the carrots have softened.