Add olive oil to large dutch oven over low-medium heat.
Add garlic and onion stirring to coat with olive oil. Do not brown, you are looking to soften the vegetables, about 5 minutes
Raise heat to medium and add carrots, celery, potatoes, kale, Swiss chard, and green beans, and 1 1/2 cups of chicken broth and tomatoes. Stir to toss and coat vegetables.
Let cook, stirring occasionally, for 8-10 minutes.
Add beans, herbs and remaining chicken broth, and stir to combine, set to simmer, stirring occasionally making sure to scrape bottom of pan. Cook 25-30 minutes or until reduced and the sauce has thickened.
Preheat oven to 350*
Once sauce is thickened, add sourdough slices into sauce, layering in a circular direction.
Tuck bread one piece of time into sauce so that you can no longer see it. Try not to overlap bread.
Sprinkle grated Parmesan over the top, drizzle with olive oil and bake for 20 minutes in the oven.
Remove, let cool, spoon up into bowls and enjoy.
You can always sprinkle on a bit more parmesan and drizzle of olive oil over bowls.