Dice the onion, carrots, and celery into small, even pieces. Mince the garlic, cube the potatoes (keep them in cold water), slice the sausage into 1/2 inch rounds, chop the kale, and drain and rinse the beans.
Heat olive oil in a Dutch oven over medium-high heat. Add the sliced sausage in a single layer and cook 4 to 5 minutes, stirring occasionally, until golden brown. Transfer the sausage to a plate, leaving the browned bits in the pot.
Reduce the heat to medium and add the onion, carrots, and celery. Stir to scrape up the browned bits and cook 6 to 8 minutes, until the onion is soft and translucent. Add a small pinch of salt.
Stir in the minced garlic, Italian seasoning, and red pepper flakes. Cook about 1 minute, stirring constantly, until fragrant. Watch closely so the garlic does not burn.
Pour in the chicken broth and diced tomatoes with their juices. Add the drained potatoes, rinsed beans, bay leaf, and Parmesan rind. Bring to a gentle boil over high heat.
Reduce heat to medium-low, partially cover, and simmer 15 to 18 minutes until a fork slides easily into a potato cube. For a thicker soup, mash a few potatoes and beans against the side of the pot.
Return the browned sausage and any juices to the pot. Stir in the chopped kale a handful at a time. Simmer uncovered 8 to 10 minutes until the kale is tender and the sausage reaches 165°F.
Remove and discard the bay leaf and Parmesan rind. Stir in the lemon juice, then taste and season with salt and black pepper. Ladle into bowls and top with freshly grated Parmesan.