Roast Vegetables: Toss sweet potatoes, shallots, and garlic in olive oil. Spread on a baking sheet. Roast at 450°F for 25 minutes, flipping halfway through.
Blend Sauce: Blend the roasted veggies with hot chicken stock and tarragon until smooth. Add cream, salt, and pepper, then blend again.
Cook Sauce: Pour the puree into a saucepan, heat, then stir in butter and Parmesan until smooth. Season with salt and pepper.
Cook Pasta: Cook fettuccine according to package directions. Toss with sauce while hot.
Serve: Garnish with extra Parmesan and tarragon. Serve immediately!