Fill a large pot with water and 2 tablespoons salt and set over high heat.
Heat a large skillet over medium high heat. When hot, add the buckwheat and toast for about 3-4 minutes or until lightly brown and nutty smelling. Set aside in a small bowl.
In the same skillet, add the butter to the pan and melt until foam subsides and butter is starting to brown, about 3 minutes. Add the olive oil, then the mushrooms. Stir to coat in the butter.
When the mushrooms start cooking, start cooking the pasta. Add the dry pasta, stir and set a timer as directed on the package.
Continue stirring the mushrooms, cooking them for about 12-15 minutes. Add the garlic when mushrooms are just beginning to brown. Cook until mushrooms are golden brown. Remove from heat if pasta is not done cooking yet. If pasta is done, add drained pasta to the mushrooms (reserve some of the pasta cooking water) and cook over medium heat.
Add the shallots and stir to combine and coat pasta in butter. If things look a little dry, add 1/4 to 1/2 cup pasta cooking water and toss everything together. Season with more pepper and salt, if needed.
Divide between four bowls and garnish with grated parmesan and the toasted buckwheat. Drop an egg yolk in the center of the pasta (if using) and serve. Direct guests to break the yolk to create a sauce.