Place a large non-stick frying pan over a medium heat and add the sliced mushrooms. Dry fry for about 5 minutes, stirring occasionally, or until softened. They will release a lot of liquid as they cook, so continue frying until the liquid evaporates. Season with salt and freshly ground black pepper, to taste.
Add the butter, garlic and thyme and sauté for 2-3 minutes, stirring often, until the garlic is fragrant and golden. Remove from the pan and set aside.
Next, boil the pasta according to packet instructions (until al dente).
Meanwhile, make the creamy cheese sauce: melt the butter in the same pan you used to fry the mushrooms. Add the flour and cook out over a medium heat, whisking constantly, for a couple of minutes. Gradually pour in the milk, whisking until you have a smooth, creamy sauce. Sprinkle in the cheese and whisk until melted.
Drain the pasta, reserving the pasta water. Add the reserved mushrooms and drained pasta to the creamy cheese sauce with a splash. Toss well to coat. Add a splash of the pasta water to loosen.
Stir in the parsley and season to taste.
Divide between 2 pasta bowls, sprinkle with grated cheese and crispy fried sage leaves. Carefully top each bowl with an egg yolk. Enjoy!