To prepare ragout, pour boiling water over porcini; let stand 20 minutes. Strain through a sieve into a bowl; reserve liquid. Finely chop porcini; divide in half.
Melt 2 teaspoons butter in a large nonstick skillet over medium heat. Add 1/2 cup shallots, garlic, and thyme; cook for 1 minute, stirring frequently. Add parsnips; cook 2 minutes, stirring occasionally. Add button mushrooms; cook 10 minutes, stirring occasionally. Add half of porcini and 1/2 cup wine; bring to a boil. Cover, reduce heat, and cook 15 minutes or until parsnips are tender. Stir in parsley, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Set aside; keep warm.
Preheat oven to 450°.
To prepare beef, rub 1/2 teaspoon salt and 1/2 teaspoon pepper over tenderloin. Heat a large ovenproof skillet coated with cooking spray over medium-high heat. Add tenderloin; cook 5 minutes, browning on all sides. Bake at 450° for 20 minutes or until a thermometer registers 140° (medium-rare) or desired degree of doneness. Place tenderloin on a cutting board; cover loosely with foil. Let stand 10 minutes. (Temperature of tenderloin will increase 5° upon standing.)
To prepare sauce, melt 1 teaspoon butter in pan over medium-high heat. Add carrot and 1/3 cup shallots; sauté 3 minutes. Add reserved porcini liquid, remaining porcini, 1/4 cup wine, and broth; bring to a boil. Cook until reduced to 1 1/2 cups (about 10 minutes). Stir in 1/4 teaspoon salt and 1/4 teaspoon pepper. Thinly slice beef; serve with ragout and sauce.