¾ cup freshly shredded Parmigiano-Reggiano cheese, divided
Heat a large skillet over medium heat and add the olive oil. Add the mushrooms and season with salt and pepper and cook until golden browned, about 10-12 minutes.
Stir the garlic into mushrooms and cook for 1 minute; pour in white wine and cook until wine is nearly evaporated. Mix chicken stock into mushroom mixture; season with salt and pepper. Bring to a simmer, reduce heat, and cook until slightly thickened, about 5 minutes.
Pour the heavy cream into mushroom mixture and stir to combine. Simmer for 5 minutes until the mixture starts to foam.
While the mushrooms are finishing cooking, fill a large pot with water and bring to a rolling boil. Stir in the Delallo fettuccine and cook until al dente, about 8 minutes. Drain but do not rinse pasta; transfer to a large serving bowl and keep warm.
Stir thyme and chives into mushroom sauce and turn off heat; mix 1/2 cup Parmigiano-Reggiano cheese into sauce until cheese has melted.
Pour all the mushroom sauce and half the mushrooms over pasta, reserving about half the mushrooms in the skillet. Toss pasta in sauce until coated; top with remaining mushrooms and remaining Parmigiano-Reggiano cheese for garnish.