Melt the butter in a large stockpot over medium heat. Add the onions and cook until softened, about 5 minutes. Add the garlic and cook until fragrant, about 2 minutes. Add the flour and cook until lightly toasted, about 2 minutes. Add the cognac and scrape the pan with a wooden spoon to release any browned bits.
Add the potatoes and broth to the stockpot and bring to a boil. Reduce the heat and simmer until the potatoes are tender, about 15 minutes.
Add the tomatoes and their juices, cream, gorgonzola and basil. Season with salt and pepper. Using an immersion blender, or in batches in a blender, puree until smooth. Add the vinegar and serve in warm bowls with more basil and gorgonzola.
Photograph by Yunhee Kim
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
Recipe courtesy Saks Cafe & Restaurant, Anchorage, AK for Food Network Magazine