In a bowl, soak the potato chunks in cold, salted water (while preparing your other ingredients). This will help to remove excess starch, and prevent the potatoes from browning.
In a heavy bottom pot, or large, deep skillet, heat a tablespoon of oil until hot. Add in the chicken, and spread out in a single layer. Sear to brown the chicken before flipping over to sear the other side. When the pieces are nicely browned, transfer them to a bowl, and set aside.
Swirl in another tablespoon of oil into the same pot, and add in onion. Sauté over medium-high heat until the onions are softened.
Add in small splashes of water if it gets too dry. Cook for about 10 minutes. [If you have the time, keep cooking the onions for another 10 minutes or so, to really soften and caramelize them]
Add in the garlic and ginger. Cook for a minute until fragrant. Then add in the carrots and sauté for another minute.
Return the chicken to the pot, and add in the chicken broth. Bring it to a boil over high heat, and then reduce it to a simmer.
Grate the peeled apple over the curry. Then add in the salt, stir well, and let simmer for 10 minutes.
Drain the salt water from the bowl of potatoes. Then add the potatoes into the curry, cover the pot, and simmer until potatoes are tender (about 15-20 minutes).
While the curry is simmering, take out a small saucepan. Add in the butter and heat over medium. Once the butter begins to melt, add in the flour to make the roux. Use a spatula to mix constantly until no lumps remain.
Once the roux starts to bubble and turn light brown, add in our Japanese Curry Powder. Mix well, so the roux forms into a thick curry paste. Just heat for a moment to allow the spices to roast and release more aroma & flavor. Remove from heat.
Add the roux into the curry. Stir well to combine. Add in honey, Worcestershire sauce (or soy sauce), and tomato paste.
Taste, and adjust any seasonings or liquid. Continue to simmer over medium-low heat until the curry thickens to a stew-like consistency. Serve the curry with Japanese rice or brown rice.