Step 1In a large, heavy-bottomed pot, heat the olive oil and butter over medium heat. Add the onion, shallots, carrot, celery and fennel and cook until softened, stirring occasionally, about 5 minutes. Stir in the minced garlic and continue to cook for 1 minute until aromatic.
Step 2Add the diced tomatoes with their juices, along with the lemon juice, sugar, paprika, gin and 1 1/2 teaspoons salt. Cook, stirring frequently, until the tomato liquid reduces and the mixture has thickened slightly, 10 to 12 minutes. Cool slightly.
Step 3Transfer the vegetables, in batches, to a blender jar and puree until smooth, then return to the pot. Add the broth, one cup at a time, until the soup reaches desired consistency, stirring to thoroughly combine.
Step 4Bring the soup to a gentle simmer over medium heat, stirring frequently. Add the cream if desired and adjust the seasoning to taste with salt and black pepper. Garnish each serving with basil.
Middle Eastern: Omit the cream and basil. Add one-fourth to one-half cup of cooked rice to each bowl. To serve, top with chopped mint and a dollop of plain yogurt.
Moroccan: Omit the cream and basil. Add 1 tablespoon each of fresh grated ginger and ground cinnamon when cooking the vegetables. To serve, top with chopped cilantro and diced Moroccan olives.
Latin American: Add 2 teaspoons ground cumin and 1 teaspoon crumbled dried oregano when cooking the vegetables. Substitute lime juice for the lemon juice. To serve, top the finished soup with 1 tablespoon of crumbled cotija or grated queso blanco, diced avocado and chopped cilantro.