Heat a pot with one tablespoon of canola oil over medium-high heat. Add the onions and cook until softened, about five minutes. Add the potatoes and carrots, toss together, and cook for five minutes to slightly heat the vegetables.
Add the vegetable broth. Bring to a boil, then reduce the heat to have the liquid at a simmer. Place the lid slightly ajar and simmer for 20 minutes. Add the curry paste and coconut milk and mix well.
Add the bok choy and simmer for an additional five minutes or until the bok choy is softened. Serve in a bowl with cooked rice or udon. Top with chives.