Cook the udon noodles according to packaging's instructions. Transfer to a bowl and set aside.
In a small bowl, combine the red pepper paste, low-sodium soy sauce, and sesame oil. Set aside.
In a pan, heat about 2 tbsp of unsalted butter over medium high heat. Once the butter has melted and starts to slightly bubble, add the garlic and onions and stir fry until fragrant and tender, about 1 minute. Add all-purpose flour and stir for another minute, or until there is no more visible uncooked flour. Pour the dashi broth and stir using a whisk until well combined. Add in the shiitake mushrooms and let cook in the sauce for about 2 minutes. Pour the cooking cream, stir, and let sauce come to a simmer and thicken. Season with white pepper and mix well. Stir in the cooked udon noodles and mix until all the noodles are equally covered with the sauce.
Serve in a bowl with chopped green onions.