First, roughly chop the onion and carrot. In a large pot over medium heat, add butter, onion, and carrot. Cook the vegetables for 5 minutes while stirring occasionally.
Add crushed tomatoes and chicken/vegetable broth to the pot and cook for 5 more minutes. Use an immersion blender to blend the soup. Add light cream to the soup and gently stir to mix. Cook for an additional 5 minutes. The tomato soup is now ready.
While the tomato soup is cooking, make the grilled cheese. Slice the bread into 1/2 inch-thick slices. Heat a panini grill, griddle, or pan over medium heat. Spread mayonnaise on one face of the sliced bread. Put two slices of bread together, mayonnaise side out, with two slices of Muenster cheese between. Place the sandwich on the grill and toast for 10 minutes. Or, if using a griddle or a pan, toast the sandwich for 5 minutes, flip, and toast for 3 additional minutes. The cheese should be melted and the outside of the sandwich will be golden brown.