Heat oven to 350°F. Place beef Ribeye Roast, fat side up, in shallow roasting pan. Insert ovenproof meat thermometer so tip is centered in thickest part of beef, not resting in fat or touching bone. Do not add water or cover. Season with salt and pepper, as desired. Roast 1-3/4 to 2 hours for medium rare; 2 to 2-1/4 hours for medium doneness.
Remove roast when meat thermometer registers 135°F for medium rare; 145°F for medium. Transfer roast to carving board; tent loosely with aluminum foil. Let stand 15 to 20 minutes. (Temperature will continue to rise about 10°-15°F to reach 145°F for medium rare; 160°F for medium.)
Meanwhile, place carrots, rutabaga and water in medium saucepan. Cover and cook over medium heat 13 to 15 minutes. Combine butter, brown sugar, lemon juice, lemon peel, dill weed and 1/4 teaspoon salt in small pan; cook over medium heat 2 to 3 minutes, stirring occasionally.
Add butter mixture to vegetables; continue cooking, uncovered, 3 to 4 minutes or until vegetables are glazed, stirring occasionally.
Carve roast into slices; season with salt and pepper, as desired. Serve with vegetables.
Nutrition information per serving: 236 Calories; 113.4 kcal Calories from fat; 12.6 g Total Fat; 5.4 g Saturated Fat; 0.6 g Trans Fat; 0.8 g Polyunsaturated Fat; 5.3 g Monounsaturated Fat; 76 mg Cholesterol; 132 mg Sodium; 6 g Total Carbohydrate; 1.3 g Dietary Fiber; 25 g Protein; 2.1 mg Iron; 445 mg Potassium; 5.6 mg NE Niacin; 0.5 mg Vitamin B6; 2 mcg Vitamin B12; 6.3 mg Zinc; 31.2 mcg Selenium; 55 mg Choline;