Prepare the tomatoes: Set one beautiful tomato aside for garnish. To easily peel the rest, bring a pot of water to a boil. Score a small 'X' on the bottom of each tomato and blanch them in the boiling water for about 30-60 seconds, until the skins begin to split. Immediately transfer them to an ice water bath to stop the cooking.
Once cool, the skins will slip right off. Core the peeled tomatoes and give them a coarse chop.
Build the flavor base: In a large saucepan or Dutch oven, melt the butter over medium heat.
Add the minced garlic and sauté for 30 seconds until fragrant, being careful not to burn it.
Add the chopped onion and cook, stirring frequently, for 4-5 minutes until softened and translucent.
Stir in the chopped, peeled tomatoes.
Bring the mixture to a boil, then reduce the heat to low, cover, and let it simmer for 30 minutes.
Stir occasionally to prevent sticking.
Once simmered, remove from heat and let it cool slightly.
Blend to perfection: Carefully transfer the tomato mixture to a blender or food processor in batches.
Blend until it reaches your desired consistency—I prefer it almost completely smooth. You can also use an immersion blender directly in the pot for easier cleanup. Return the puréed soup to the saucepan.
Make it creamy and rich: Finely chop all the fresh basil and set aside about 1/4 cup (960 ml) for garnish.
Stir the remaining basil, sea salt, and black pepper into the soup. Gently heat the soup over low heat.
Stir in the shredded Gruyère, heavy cream, and the optional Armagnac.
Continue stirring gently just until the cheese is completely melted and the soup is creamy.
Do not let it boil, as this can cause the cream to separate.
Garnish and serve: Finely chop the reserved fresh tomato. To serve, ladle the hot soup into bowls.
Garnish each serving with a sprinkle of the chopped fresh tomato and the reserved fresh basil.
Serve immediately with a side of crusty bread for dipping.
Grate your own cheese from a block. Pre-shredded cheeses often contain anti-caking agents that can prevent them from melting smoothly into the soup.