Heat olive oil in a grill pan over medium-high heat. Spread 1/2 tablespoon butter over 1 side of each bread slice. Turn the slices over and top 2 slices with cheddar and place remaining 2 slices of bread on top, buttered sides up. Add sandwich to pan and grill until the bread is golden and the cheese is melted, about 2-3 minutes per side. Let cool for 1 minute and cut into 1-inch cubes.
Heat olive oil in a large stockpot or Dutch oven over medium heat. Add onion, garlic, red pepper flakes and bay leaf and cook, stirring frequently, until onion is translucent, about 3-5 minutes.
Stir in tomatoes and mash, using a potato masher, until broken down into smaller pieces. Stir in heavy cream and brown sugar.
Bring to a boil; reduce heat and simmer until slightly thickened, about 8-10 minutes. Remove bay leaf.
Puree with an immersion blender. Stir in vegetable broth until heated through, about 2 minutes; season with salt and pepper to taste.
Serve immediately with “croutons,” garnished with parsley.