Step 1: Sauté the onion and garlic in olive oil in a large pot over medium heat until the onion becomes translucent and the garlic is fragrant (about 5-7 minutes).
Step 2: Add the chopped fresh tomatoes (or canned tomatoes), fresh thyme, salt, and pepper. Stir to combine and cook for 10-15 minutes, allowing the tomatoes to break down.
Step 3: Pour in the vegetable broth and bring the mixture to a boil. Reduce the heat and let it simmer for another 10-15 minutes.
Step 4: Blend the soup using an immersion blender until smooth and creamy, or transfer it in batches to a regular blender. Taste and adjust seasoning with salt, pepper, or sugar.
Step 5: Once the soup is blended, return it to the heat and stir in the shredded pepperjack cheese. Let it melt into the soup, creating a creamy texture.
Step 6: For extra richness, add the heavy cream and stir until fully combined. Garnish with fresh basil and serve hot.