Cook the vegetables:
Heat the olive oil in a Dutch oven or large pot over medium heat for 1 minute. Add the onion, carrot, and celery. Cook for 4-5 minutes until the vegetables soften slightly and the onion becomes translucent.

Add seasonings:
Add the minced garlic, dried oregano, basil, and chili flakes (if using). Cook for an additional 2 minutes to release the flavors.

Add peppers and broth:
Roughly chop the roasted red peppers and add them to the pot. Stir in the tomato paste and vegetable stock. Bring the mixture to a boil over high heat, then reduce to a simmer for 10 minutes.

Blend the soup:
Blend the soup to your desired smoothness using an immersion blender directly in the pot, or blend in batches using a regular blender with the vent loosely covered with a tea towel. For an even smoother texture, strain the soup through a fine mesh strainer, pushing through as much of the soup as possible.

Finish the soup:
Return the soup to the pot over medium heat. Add the thickened cream and shredded gouda cheese, stirring for 3-4 minutes until the cheese is melted and the soup is hot.

Taste and season:
Taste the soup and add salt, pepper, and 1-2 tablespoons of the red pepper brine (or a bit of sherry vinegar/red wine vinegar) to adjust the flavor. Add more salt and pepper as needed.

Serve:
Serve immediately with buttered toast, croutons, or grilled cheese on the side.