In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes, or until the onion is translucent.
Add the minced garlic and sauté for an additional 1-2 minutes, until fragrant.
Stir in the roasted red peppers and vegetable broth. Bring the mixture to a simmer and cook for about 10 minutes.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a countertop blender.
Return the pureed soup to the pot over low heat. Stir in the heavy cream, shredded gouda cheese, dried basil, salt, black pepper, and balsamic vinegar. Cook for an additional 5-10 minutes, stirring occasionally, until the cheese is melted and the soup is heated through.
Taste and adjust seasoning if necessary. Serve hot, garnished with extra gouda or fresh basil if desired.