Cut potatoes into approximately 2-inch chunks. Transfer to a large bowl, cover with water, and swish potatoes around to remove dirt and excess starch. Drain well. Peel carrots and cut into 2-inch pieces. Peel onion and cut into 2-inch wedges.
Preheat oven to 425 F. In a large roasting pan, toss potatoes, carrots, onion, and garlic with olive oil. In a medium bowl, whisk cornstarch with a small amount of the beef broth until smooth, then whisk in remaining broth. Pour broth over vegetables in roasting pan, then sprinkle with thyme, salt, and pepper. Cover pan with foil and bake 40 minutes. Pull pan out of oven and remove foil. Place sausages on top of the vegetables, leaving space between them. Bake 8 minutes, then flip sausages over and bake another 6 minutes, or until the internal temperature of the sausages reaches 160 F, vegetables are soft, and gravy is thickened.
Per serving: 480 calories, 33 grams fat (10 grams saturated fat), 31 grams total carbohydrates, 64 milligrams cholesterol, 1,459 milligrams sodium, 6 grams fiber, 17 grams protein.
