To make the soup, heat the 2 tablespoons (30ml) olive oil in a Dutch oven or large, heavy-bottomed pot over medium-high heat. When shimmering, add the mushrooms, stir to coat in the oil, and cook, undisturbed until starting to turn golden brown, 8 to 10 minutes.
Reduce the heat to medium, move the mushrooms to one side of the pan, add 2 tablespoons (30ml) olive oil in the empty space and, when shimmering, add the fennel seeds, then cook, stirring frequently, until they turn a shade darker, 15 to 45 seconds.
Add the carrot, onion, fennel, half the garlic, and 1 teaspoon salt, stir, and cook, stirring occasionally, until the vegetables soften, 8 to 12 minutes.
Add the wine, if using, tomato paste and garam masala, and cook, stirring occasionally, until the wine has evaporated by half, 2 to 4 minutes.
Stir in the stock, lentils, soy sauce, thyme, and the remaining 1 teaspoon salt, increase the heat to medium-high, and bring to a boil. Cover, reduce the heat to medium, and simmer until the lentils are cooked through, 35 to 45 minutes.
Meanwhile, prepare the topping. Heat the remaining 2 tablespoons (30ml) olive oil in a tadka spoon or small skillet, add the remaining half of the garlic, and cook, stirring or swirling occasionally, until the garlic turns light golden.
Pour the garlic and oil into a small bowl. Zest 1 lemon into the bowl, then squeeze the juice of half the lemon into the bowl. Add the parsley and Calabrian chile paste and stir to combine. Taste and season with salt, to taste. Set aside.
To finish the soup, transfer 1½ cups (355ml) of the cooked soup to a blender. Starting on low and increasing to high, blend until smooth and then pour back into the pot with the rest of the soup.
Stir in the juice of the remaining half of the lemon, taste, and season with salt, if necessary.
To serve, ladle into individual bowls, garnish with a dollop of sour cream, labneh, or yogurt, if desired, and spoon some of the reserved saucy topping over the top. Serve with crusty bread for dipping.
