How to Make It
Preheat oven to 425°.
Bring stock to a boil in a small saucepan over medium-high heat; add porcini mushrooms. Remove pan from heat; let stand 15 minutes. Drain stock mixture in a colander over a bowl; reserve stock mixture. Chop porcini mushrooms; set aside.
Remove giblets and neck from turkey; discard liver. Pat turkey dry with paper towels; trim and discard excess fat. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Combine 3 tablespoons butter, 1 tablespoon minced garlic, rosemary, 1 teaspoon salt, and 1/2 teaspoon pepper in a bowl. Rub butter mixture under loosened skin and over breasts and drumsticks. Lift wing tips up and over back; tuck under turkey. Tie legs together with kitchen string. Place reserved giblets, neck, 10 garlic cloves, onion, celery, and carrots in the bottom of a large roasting pan; add stock mixture to pan. Place roasting rack in pan; coat with cooking spray. Arrange turkey, breast side up, on roasting rack. Bake at 425° for 30 minutes. Cover turkey loosely with foil. Reduce oven temperature to 325° (do not remove turkey from oven). Bake 1 hour and 10 minutes or until a thermometer inserted into meaty part of thigh registers 165°. Remove pan from oven; place turkey on a cutting board. Let stand, covered, 20 minutes. Carve turkey.
Place a large zip-top plastic bag inside a 4-cup glass measure. Strain stock mixture through a sieve into bag; discard solids. Let stand 10 minutes. Seal bag; snip off 1 bottom corner of bag. Drain stock mixture into a bowl, stopping before fat reaches opening.
Heat a large nonstick skillet over medium-high heat. Add oil; swirl to coat. Add reserved porcini and shiitake mushrooms to pan; sauté 8 minutes. Add Madeira; cook 1 minute. Add stock mixture to pan; bring to a boil. Cook 3 minutes. Combine remaining 2 tablespoons butter and flour in a small bowl. Gradually add butter mixture to stock mixture, stirring constantly with a whisk. Cook 2 minutes. Stir in remaining 1/2 teaspoon salt and remaining 1/4 teaspoon pepper. Serve gravy with turkey.