Bring a large pot of salted water to a boil. Add the spaghetti and cook it according to the package directions, until al dente. Drain the pasta into a colander when done, reserving at least a half cup of the pasta cooking water.
While the pasta boils, coat the bottom of a large skillet with the olive oil and place it over medium heat. Add the sliced shiitakes in an even layer. Let them cook for 4 to 5 minutes, undisturbed, then flip and let them cook another 4 to 5 minutes, until tender and lightly browned.
While the mushrooms cook, place the miso paste, coconut cream, and vegan butter into a small bowl, then whisk or stir them together with a fork. Set this aside for now.
Once the mushrooms have browned, push them to the side of the skillet, then add the garlic to the space you just created. Sauté the garlic for about 1 minute, stirring constantly.
Add the pasta to the skillet, along with the miso mixture and about ½ cup of the reserved pasta cooking water. Stir everything well with a fork and bring the liquid to a boil. Lower the heat and let it simmer for a minute or two, until most of it has cooked off and the sauce has turned smooth and silky.
Take the skillet off the heat. Stir in the peas and black pepper. Taste-test and optionally season with salt to taste.
Divide onto plates and serve.