In a medium pot, heat 2 tablespoons olive oil over medium-high heat. Add the onion and cook until softened, about 3 minutes. Stir in the carrot, cover and cook for 5 minutes more. Add the tomatoes and vegetable broth, bring to a simmer, cover and cook until the vegetables are soft, about 20 minutes. Stir in the cream and, using an immersion blender, puree until smooth; season with salt and pepper.
Meanwhile, in a large skillet, heat 1 tablespoon olive oil over medium-high heat. Add the kale, season with salt and pepper and cook, stirring often, until tender, about 5 minutes. Remove from the heat.
Preheat a grill pan over medium heat. On a work surface, layer each of 4 bread slices with 1 slice of cheese and some of the kale, then top with a second slice of cheese and bread. Brush the outside of the sandwiches with the remaining 3 tablespoons olive oil. Grill, turning once, until the cheese is melted and grill marks appear, about 5 minutes. Serve with the tomato soup.
