Step 1

Trim the leeks, discarding the tough green tops, halve vertically, and rinse in cold water, making sure to clean out any dirt trapped between the layers. Slice into thin half circles.

Step 2

In a large Dutch oven or heavy skillet over medium heat, warm the olive oil. Add the leeks and celery, and cook until the vegetables are softened, 3 to 5 minutes. Add garlic and cook for an additional minute.

Step 3

Add the beans, thyme, herbes de Provence, salt, and pepper. Pour in the vegetable broth and bring the mixture back up to a gentle simmer. Cook for approximately 25 minutes (stirring occasionally) or until almost all of the liquid is gone.

Step 4

Arrange a rack in the lower third of your oven and preheat the oven to 400 degrees F.

Step 5

Sprinkle the Parmesan on top of the bean mixture and place the pot in the oven, leaving the lid off. Cook until the cheese is completely melted and brown in spots, around 10 minutes. Sprinkle with red pepper flakes (if using). Serve warm.