Preheat oven to 300 degrees F (150 degrees C).
Combine melted butter, Italian seasoning, olive oil, and salt in a large bowl
Add sourdough bread cubes and toss to coat. Sprinkle Parmesan cheese over the bread cubes; toss to coat. Spread onto a baking sheet.
Bake in preheated oven, stirring occasionally, until lightly browned, about 20 minutes.
As the croutons are baking, cut the green cabbage into strips and lay them out on a plate. Sprinkle generously with parmesan cheese shavings and sourdough croutons.