Make the tomato soup: Heat olive oil in a Dutch oven over medium/high heat. Add the onion to the pan and season with ½ teaspoon of salt. Cook the onions down until translucent, 7-9 minutes.
Add the tomato paste and garlic to the onions and saute for an additional 2 minutes.
Next, add the crushed tomatoes, peeled tomatoes, chicken broth, Worcestershire, and brown sugar to the pot. Stir to combine. Bring the mixture to a boil over medium/high heat.
Turn the heat to low and allow the soup to simmer for 5 minutes.
Transfer the soup to a high-speed blender (we prefer a Vitamix) and carefully blend the soup until completely smooth.*
Transfer the soup back to the Dutch oven and allow the soup to warm over medium/low heat while you prepare the grilled cheese.
Make the grilled cheese: Place two cheddar cheese slices and one slice of gouda on top of one slice of bread, and then place the second piece of bread on top of the cheddar cheese. Spread butter on the top of the top slice.
Next, heat a large skillet over medium heat. Add the grilled cheese, butter-side-down, to the pan and let it cook for 3-4 minutes over medium heat. While it's cooking, spread a generous amount of mayo on top of the top slice.
Flip the grilled cheese and cook for an additional 2-4 minutes on the other side. We like to cover the grilled cheese to make sure the cheese melts.
Slice each grilled cheese sandwich in half, and serve alongside the tomato soup.