Make the soup:
Toast the fennel seeds in a small skillet over medium heat until they release their aroma and are golden brown, 2 to 3 minutes. Pound them coarsely in a mortar or grind them coarsely in a spice grinder.
Heat a 6- to 8-qt. heavy-bottomed pot over high heat for 2 minutes. Pour in 1/2 cup olive oil and add the rosemary leaves and chile. Let them sizzle in the oil for about 1 minute. Add the onion, fennel, fennel seeds, and 1 Tbs. thyme and cook until the onion is softened, 3 to 4 minutes.
Add the beans to the pot and cook a few more minutes, stirring to coat well. Add 3 quarts of water, and bring to a boil over high heat. Turn the heat to low and place a circle of parchment over the beans to keep them underwater. Simmer, stirring occasionally. After 30 minutes, add 1-1/2 Tbs. salt to the beans, and continue cooking at a low simmer until the beans are tender, 1 to 1-1/2 hours.
While the soup is cooking, stir together the mascarpone, minced shallots, and chives in a small bowl. Season to taste with salt and pepper, cover with plastic wrap, and refrigerate.
Separate the bean mixture from the liquid by straining the soup over a bowl. Put half the bean mixture into a blender with 1/2 cup of the liquid (you will need to purée the soup in batches). Process on the lowest speed until the mixture is puréed. With the blender running at medium speed, slowly pour in more of the liquid, until the soup is the consistency of heavy cream. Turn the speed up to high, and blend until completely smooth, about 1 minute. Set aside, and repeat with the second batch. (Save any extra liquid for thinning the soup later, if necessary.) Taste and adjust the seasoning with salt and pepper. Keep the soup warm in a pot on the stove. If making ahead, cool completely before refrigerating.
Sauté the mushrooms:
If making the soup ahead, save the leftover cooking liquid. The soup will thicken as it sits and may need to be thinned with more of the liquid before serving. If necessary, adjust the seasoning as well.
Turn on the exhaust fan. Heat a 12-inch skillet over high heat for 1 minute. Swirl in the remaining 2 Tbs. olive oil and the butter. When the butter melts, scatter the mushrooms into the pan. Season with 1/4 tsp. salt and a pinch of pepper. Cook the mushrooms, stirring occasionally, until they are tender, browned, and a little crispy, about 5 minutes. Stir in the parsley and the remaining 1 tsp. thyme and remove from the heat.
Ladle the hot soup into warm bowls. Scatter warm mushrooms over the top and add a dollop of the mascarpone.
The soup and chive mascarpone can be made up to one day in advance and refrigerated. The mushrooms can be sautéed a few hours in advance. Reheat the soup and mushrooms just before serving.