Melt butter in a large pot or saucepan over medium heat. Once the butter has melted, add the onion and garlic, and sauté until fragrant, about 1 minute.
Sprinkle flour into the pot, stir to combine with the veggies, and continue to cook for 1 minute more, creating a roux.
Add the stewed tomatoes, evaporated milk, and broth and stir to combine.
Bring the mixture to a low simmer, stirring frequently and cook for 15 minutes or until the soup has thickened slightly and the veggies are tender.
Carefully transfer the soup (working in batches if necessary) to a blender and puree until smooth.
Return the soup to the pot, season to taste with salt and pepper, and keep warm, on low heat, until ready to serve.
For the grilled cheese, melt butter in an extra large skillet over medium-high heat. (Work in batches if needed to accommodate all 4 sandwiches).
Once the butter has melted, add half of the bread slices to the skillet, and distribute cheeses between the slices.
Cap sandwiches with the remaining bread slices and gently press to compress the cheese.
Toast for 1-2 minutes per side or until golden brown, crispy, and super melty.
Divide soup and grilled cheese between plates and bowls. Garnish soup with fresh basil before serving.