Preheat the oven to 180°C (350°F).
Wipe the mushrooms clean with a damp cloth, then slice each mushroom in half. Finely mince the garlic and chop the chives. Measure the heavy cream, milk, sour cream, and remaining ingredients so they are ready for cooking.
Place a large skillet over medium-high heat and melt the 2 tablespoons of butter.
Once the butter begins to foam, arrange the halved mushrooms in a single layer. Leave them undisturbed for 3–4 minutes, allowing one side to become deeply golden.
Stir the mushrooms and continue cooking for another 3–4 minutes, or until they are tender and have released their moisture.
Add the 2 teaspoons minced garlic to the browned mushrooms and cook for approximately 30 seconds, just until aromatic.
In a small bowl, combine the 2 tablespoons cornstarch with several tablespoons of the measured milk. Whisk until completely smooth to form a lump-free slurry.
Pour the cornstarch slurry into the skillet, followed by the remaining milk and the 1 cup heavy cream. Stir continuously as the mixture comes together.
Allow the sauce to simmer gently for 3–5 minutes, stirring frequently, until it thickens sufficiently to coat the back of a spoon.
Stir in 2–3 tablespoons fresh lemon juice, using the amount that best suits your preferred level of acidity. Adding the lemon at this stage allows its sharpness to soften slightly as it blends into the creamy sauce.
Remove the skillet from the heat. Stir in the 1 cup sour cream until smoothly and completely incorporated. Keeping the pan off the heat at this stage helps prevent the sour cream from separating.
Fold in the ½ cup chopped chives, then season the mixture with salt and freshly ground black pepper according to taste.
Add the 1 pound cooked pasta and gently fold everything together until the pasta is thoroughly covered with the mushroom cream sauce.
Transfer the creamy mushroom pasta mixture to a baking dish and spread it evenly.
Scatter the 1 cup freshly grated mozzarella uniformly over the surface.
Bake in the preheated oven for 20 minutes, or until the mozzarella is melted, bubbling around the edges, and lightly golden across the top.
Remove the pasta bake from the oven and allow it to stand for 2–3 minutes before serving. This brief resting period gives the creamy sauce time to settle slightly and helps the pasta maintain its structure when portioned.