Heat oil in large saucepan over medium-high heat. Add onion and carrot; cook 2 to 3 minutes or until onion is tender. Add garlic; cook 1 minute more or until fragrant.
Add water, tomato sauce and tomato paste to saucepan; stir to combine. Reduce heat and simmer 15 minutes or until thickened slightly, stirring occasionally.
Remove soup from heat. Carefully blend mixture in saucepan with hand-held immersion blender until smooth. Stir in milk and keep warm; set aside.
Make grilled cheese sandwiches by buttering 1 side of each bread slice. Place 1 slice each of mozzarella and Cheddar cheese on half the bread on the non-buttered side. Spread 2 tablespoons pumpkin on non-buttered side of remaining bread slices; place pumpkin side down over cheese. Cook sandwiches in large skillet over medium heat until both sides are golden brown and cheese is melted. Let sandwiches stand 2 minutes; serve with soup sprinkled with Parmesan cheese.