Heat olive oil and 1 tablespoon butter in a large skillet over medium heat. Add the sliced onions and cook, stirring often, for 15 to 20 minutes until they turn golden and soft.
In a medium saucepan, melt 1 tablespoon butter over medium heat. Add the minced garlic and cook for 1 minute. Pour in the crushed tomatoes and vegetable broth. Simmer for 10 minutes, then stir in the heavy cream. Season with salt and pepper. Keep warm on low heat.
Butter one side of each bread slice with the remaining tablespoon of butter. Layer cheese, caramelized onions, and apple slices on four slices, then top with the remaining bread, buttered side out.
Heat a clean skillet over medium heat. Cook each sandwich for 3 to 4 minutes per side until the bread is golden and the cheese has melted.
Ladle the tomato bisque into bowls and serve alongside the hot sandwiches.