Melt 2 tablespoons butter in a large pot over medium heat. Add the diced onion and minced garlic, then cook for 4 to 5 minutes until the onion turns soft and clear.

Pour in the crushed tomatoes, vegetable broth, sugar, and dried oregano. Bring the mixture to a gentle simmer and cook for 15 minutes, stirring now and then.

Remove the pot from the heat and stir in the heavy cream. Season with salt and black pepper to taste. Use an immersion blender to puree the soup until it reaches a completely smooth consistency.

Butter one side of each bread slice with the remaining 3 tablespoons softened butter. Place cheese slices between two pieces of bread to form four sandwiches, with the buttered sides facing out.

Heat a skillet over medium heat and cook each sandwich for 2 to 3 minutes per side until the bread turns golden and the cheese melts. Cut the finished sandwiches into strips for dipping.