Cook the udon noodles according to the package instructions. Drain and set aside, reserving about 1 cup of the udon cooking water.
In a large skillet or wok, melt the butter over medium heat. Add minced shallot and garlic, and sauté until fragrant and softened.
Add sliced crimini mushrooms to the skillet and cook until they release their moisture and become tender, about 5-7 minutes.
Sprinkle paprika over the mushroom mixture. Stir well to combine.
Pour in the cream and stir, allowing the cream to heat through. Add miso paste and grated Parmesan cheese, stirring until the cheese is melted and the miso is fully incorporated.
Gradually add the reserved udon water, a little at a time, until you achieve your desired sauce consistency. Season with salt and pepper to taste.
Add the cooked udon noodles to the creamy mushroom miso sauce, tossing gently to coat the noodles evenly.
Serve the creamy mushroom miso udon hot, garnished with optional poached or soft-boiled egg, chopped chives, and a sprinkle of grated Parmesan cheese.