Trim the root end and the tough, dark green top of the leek and remove any thick outer layers. Cut the leek in half lengthwise, then slice into ¼-inch (6-mm) thick half moons.
Transfer to a bowl of water and shake around with your fingers to loosen any dirt or grit. Let the leeks sit in the water for a couple minutes to let any grit to sink to the bottom of the bowl. Carefully remove the cleaned leeks from the bowl, leaving the dirty water behind.
Heat the olive oil in a large, heavy-bottomed pot over medium heat. Add the pancetta and cook until crispy and most of the fat has rendered, about 8 minutes.
Add the leeks, carrots, celery, mushrooms, and garlic. Season with salt. Cook for 5-6 minutes, until the vegetables have released their juices and begin to soften.
Add the thyme leaves, tomatoes, beans, and vegetable stock. Stir to combine, then bring to a boil, cover, and cook, stirring occasionally, for 20 minutes until slightly reduced and hot throughout. Season with more salt, to taste.
Ladle into bowls and top with freshly grated Parmesan cheese. Serve with crusty bread.