In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the chopped summer squash and diced potato to the pot. Cook for about 5 minutes, stirring occasionally.
Pour in the vegetable broth and bring the mixture to a boil. Reduce the heat and let it simmer for 15-20 minutes, or until the squash and potato are tender.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. Alternatively, you can carefully transfer the soup in batches to a blender.
Return the pureed soup to the pot and stir in the heavy cream. Season with salt and pepper to taste. Heat gently over low heat until warmed through.
Serve hot, garnished with fresh basil.