Heat oil in a large pan, skillet, or Dutch oven over medium-high heat. Add the carrots, both bell peppers, potatoes and sauté just until the edges are browned, about 2-3 minutes.
Remove the vegetables from the pan and set aside in a bowl.
Add the onions, garlic, and ginger to the pan and sauté just for 1 minute, to soften.
Add the chicken and brown on all sides.
Once the chicken has browned, remove from the pan and transfer to a bowl. Set aside.
If there are browned bits of charred garlic, onions, and ginger on the bottom of the pan, pour a little chicken stock into the pan and scrape up with a wooden spoon. If there are a LOT of browned bits, go ahead and carefully use the wooden spoon to remove them from the pan. If there are a few browned bits, it's okay to leave them in for now.
Add the remaining chicken stock, fish sauce, and coconut milk. Stir to combine.
Add the curry powder, paprika, salt, and pepper. Stir.
If you see a lot of browned bits still in the curry sauce at this point, feel free to strain the sauce through a fine mesh sieve or strainer into a large heatproof bowl. Discard the brown bits and return the curry sauce into the pan.
Add the chicken back to the pan/pot, lower the heat to medium, cover, and cook for about 20 minutes. Check on the chicken halfway through and use tongs to turn the pieces over to the other side; return the cover and continue cooking.
At 20 minutes, uncover and add the carrots, bell peppers, and potato back to the pan. Cook uncovered for about 5-6 minutes, or until the chicken is all fully cooked through (see Notes).
Serve immediately over rice.
Notes
Makes approximately 6 servings.Chicken doneness: Chicken is fully cooked when a meat thermometer inserted into the chicken meat has an internal temperature of 165°F.Storage: allow the chicken curry to cool down, then store in an airtight container in the refrigerator for up to 5 days or freeze for up to one month.