Bring a large pot of water to a boil and season with salt.
While waiting for the water to boil, heat oil in a large skillet with high sides over medium heat. Once hot, add chicken and cook until browned all over, about 5 to 6 minutes. Remove from skillet and set aside.
Add in onions and cook, stirring occasionally, until translucent. This will take about 2 to 3 minutes. Remove onions to the bowl with the chicken.
Pour in dashi. Scrape up all the browned bits on the bottom of the skillet. Stir in mirin, soy sauce, salt, and curry roux cubes. Continue to stir until the cubes have dissolved. Bring to a simmer and cook for 2 to 3 minutes.
While the sauce is simmering, cook udon noodles for about 3 minutes less than instructed on the packaging. Drain and set aside.
Return chicken and onions to the pan. Stir to combine. Simmer for 3 to 5 minutes, until it is the consistency you prefer.
Add noodles and stir to combine. Stir in coconut milk and cook until warmed through, about a minute or so.
Serve immediately with a garnish of freshly sliced green onion.