Step 1: If using dried morels, rehydrate them now. Place dried morels in a bowl and cover with warm water, milk, or vegetable broth for 20-30 minutes. Once plump, gently remove them with a slotted spoon, reserving the liquid. If using fresh morels, clean them thoroughly as described in the 'Key Ingredient Notes' section.
Step 2: Bring a large pot of salted water to a rolling boil for the pasta. Cook your preferred pasta according to package directions until al dente. Reserve about 1 cup of the pasta cooking water before draining.
Step 3: While the pasta cooks, melt 2 tablespoons of butter in a large skillet or sauté pan over medium heat. Add the cleaned and dried morel mushrooms (or rehydrated morels) to the pan. Sauté for 5-7 minutes, stirring occasionally, until they release their moisture and begin to brown slightly. Season lightly with salt and pepper. Remove the morels from the pan and set aside.
Step 4: Add the remaining 1 tablespoon of butter and the olive oil to the same skillet. Add the minced shallots and cook for 2-3 minutes until softened and translucent, being careful not to burn them. Add the minced garlic and cook for another minute until fragrant.
Step 5: Deglaze the pan with white wine (or vegetable broth). Scrape up any browned bits from the bottom of the pan – this is where much of the flavor resides! Let it simmer for 2-3 minutes until the liquid has reduced by about half. If you reserved liquid from rehydrating dried morels, now is a great time to add a splash (after straining it).
Step 6: Pour in the heavy cream and bring the sauce to a gentle simmer. Reduce the heat to low and let it simmer for 3-5 minutes, stirring occasionally, until it slightly thickens.
Step 7: Return the cooked morels to the pan with the cream sauce. Stir in the freshly grated Parmesan cheese until melted and smooth. If the sauce is too thick, add a tablespoon or two of the reserved pasta cooking water until it reaches your desired consistency. Taste and adjust seasoning with salt and freshly ground black pepper.
Step 8: Add the drained al dente pasta directly to the skillet with the sauce. Toss well to coat the pasta evenly with the creamy morel sauce. Stir in the fresh parsley and thyme just before serving to add brightness.
Step 9: Serve immediately, garnished with extra Parmesan cheese and a sprinkle of fresh herbs.