Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).

Place the halved tomatoes on a baking sheet and drizzle them with olive oil. Roast the tomatoes in the preheated oven for about 30–40 minutes, or until

they’re soft and slightly charred.

In a large pot, melt the butter over medium heat. Add the chopped onion and sauté until the onion becomes

translucent. Add the chopped garlic and cook for an additional one to two minutes.

Add the roasted tomatoes (including any juices from the baking sheet) to the pot. Stir in the vegetable broth or water, sugar, fresh basil leaves, salt, and black

pepper. Bring the mixture to a boil.

Reduce the heat to low and let the soup simmer for about 20 minutes, allowing the flavors to meld together.

Use an immersion blender to puree the soup until smooth. Alternatively, transfer the soup to a blender in batches and blend until smooth. Be careful with the hot liquid and allow the soup to cool slightly before blending if using a regular blender.

Return the pureed soup to the pot and place it over low heat. Stir in the vinegar and heavy cream if using. Cook

for an additional five minutes to heat through. Garnish each bowl with a drizzle of olive oil and some fresh basil leaves, if desired.

Preheat a skillet or griddle over medium-low heat.

Spread the softened butter evenly on one side of each slice of sourdough bread.

Place the bread, buttered side down, on the preheated skillet or griddle.

Layer the smoked cheese slices on each slice of bread, covering the surface evenly.

Top the cheese with the thinly sliced red onion and jalapeño slices.

Place another slice of bread, buttered side facing up, on top to form the sandwiches.