Make 1-inch-deep cuts into lamb. Pierce roast at 1- to 2-inch intervals, using a small paring knife. Insert a garlic slice into each cut. Sprinkle lamb with 1 teaspoon salt, pepper, and thyme; place in a roasting pan.
Place in a 450° oven. Immediately reduce oven temperature to 350°, and bake 40 minutes.
Melt 2 tablespoons butter in a large skillet over medium heat; add shallots and minced garlic, and saute 2 to 3 minutes. Add mushrooms and remaining 1/4 teaspoon salt; saute until tender and liquid evaporates. Remove from skillet, and set aside.
Cut off carrot tops, leaving 1 inch attached to carrots; scrape carrots. Add carrots, onions, and turnips to roasting pan; bake 40 more minutes or until vegetables are tender and a meat thermometer inserted into thickest portion of lamb registers 145° or to desired degree of doneness. Remove lamb and vegetables from pan, reserving drippings.
Reserve 1/4 cup chicken broth.
Add reserved drippings, remaining broth, leeks, and pea pods to mushroom mixture in skillet; cook over medium-high heat, stirring occasionally, 5 to 6 minutes.
Stir all-purpose flour into reserved 1/4 cup chicken broth; gradually stir into mushroom mixture. Cook over medium-high heat, stirring constantly, until mixture is thickened and bubbly. Serve with lamb and vegetables.