In a large round baking dish, combine beefsteak tomatoes, grape tomatoes, onion, celery, garlic cloves, and oregano leaves. Season with a generous pinch of salt and pepper, and drizzle with 2-3 tablespoons of olive oil. Stir to evenly coat the vegetables, then roast in the Blackstone Pizza Oven at 350 degrees for 15-20 minutes or until vegetables are roasted.
While the tomatoes are roasting, place the sliced onions on the griddle with a pinch of salt. Cook over medium-low heat for 15 minutes, tossing often, until caramelized and golden brown. Remove from heat.
In a large food processor, combine the roasted vegetables, heavy cream, chicken stock, basil leaves, and lemon zest. Blend until the desired smoothness is achieved.
On the griddle, melt some butter and toast one side of each bread slice. Flip the bread and assemble the sandwich on the toasted side. Start with 2 slices of gouda, followed by some caramelized onions, 2 slices of provolone, and the top bread slice. Flip and press until the sandwich is toasted to your liking.
Serve the soup with a garnish of cream, balsamic vinegar, sundried tomatoes, and fresh basil, if desired.