Heat a large, heavy-bottomed pot over medium heat. Add the sliced mushrooms and cook, turning occasionally, until they release their water and the water evaporates, about 6 to 8 minutes.
Add 3 tablespoons of butter to the mushrooms and continue sautéing for 8 to 10 minutes until they deepen in color. Season with salt and pepper.
Sauté the vegetables:
Add the diced carrots, parsnips, celery, and onion to the mushrooms and sauté for 5 minutes. Add the minced garlic and 1 teaspoon dry thyme and cook until fragrant, about 1 minute. Season generously with kosher salt and black pepper.
Coat the vegetables with 2 tablespoons of flour. Cook for 1 minute until the flour toasts lightly. Slowly add 4 cups of water, whisking constantly until incorporated.
Add the beans and bring to a boil. Reduce the heat to low. Add the bay leaves. Taste and season again with a big pinch of kosher salt.
Bake the cassoulet:
Transfer to the oven, uncovered, for 1 to 2 hours. Check the cassoulet after 1 hour and add more liquid if needed. The liquid should reduce significantly.
Make the topping:
Preheat the air fryer to 400ºF. Place the bread cubes in a large bowl and drizzle with 1 tablespoon of extra virgin olive oil and a pinch of salt. Use your hands to massage the oil into the bread. Transfer to the air fryer for 4 to 6 minutes until golden brown and toasted. See Note 1.
Transfer the toasted bread cubes to a food processor. Pulse until a fine meal forms.
Pour the breadcrumbs into a large bowl and add the minced parsley. Stir to combine. Taste and add salt. Cover the bowl and set aside until ready to serve.
Finish the cassoulet:
Remove the pot from the oven and discard the bay leaves. Taste the beans and season once more. Spoon half the herby breadcrumbs on top of the cassoulet.
To serve:
Spoon the cassoulet into shallow bowls and finish with more breadcrumbs. Enjoy!
Notes
Note 1: You can also place the bread cubes on a baking sheet and transfer them to the oven with the cassoulet. Just place the baking sheet on the unused rack and bake for 10 to 12 minutes at 350ºF.