Peel and dice the onion. To prepare the leeks, cut off the dark leaves from the top. Trim the root and wash between the layers. Chop into a small dice. Cut the zucchini into a small dice, removing any large seeds as needed. Mince the garlic and set aside.
In a wide skillet or braiser, heat the olive oil over medium heat. Add the onion and leeks and sauté for 3 to 4 minutes until they begin to soft. Add the zucchini and cook for another 4 to 5 minutes until the zucchini begins to soften. Add the minced garlic and sauté for another minute until fragrant.
Add the vegetable broth to the skillet along with the white beans. Season with the kosher salt and pepper. Bring to a simmer and cook for 10 to 15 minutes until all the vegetables are tender and the broth begins to reduce.
To make the pistou, roughly chop the basil and parsley and finely mince the garlic. Add the basil, parsley, garlic, lemon zest and juice, and kosher salt to the food processor and run until finely minced. With the motor running, stream the olive oil into the food processor and blend until the oil is fully mixed in.
After simmering the cassoulet, use a potato masher or wooden spoon to gently crush some of the beans. This will help to thicken the broth into a creamy, stew-like texture. Add the baby spinach, stirring to combine, and allow the spinach to wilt.
Remove from the heat and add about 3/4 of the pistou to the cassoulet, stirring to combine. Set aside the remaining 1/4 to use later. Taste and check the seasoning.
To serve, thin the plain yogurt with a little water. Drizzle the yogurt over the cassoulet and top with the reserved pistou. Serve with the slices of toasted bread and enjoy!