For best results, purchase the loaf of bread the day before making this stuffing and let it sit out on the counter overnight. You can roughly chop or tear it into cubes (you want ~10 cups) and let it sit out in a bowl. If you do not do this, you can toast the cubes yourself. Preheat the oven to 300 degrees F and put the sourdough cubes on 2 baking sheets. Bake for 20-30 minutes, or until they are toasted/dried out but not rock hard.
Prepare the onion, celery, carrots, mushrooms, and kale, and melt the sticks of butter in a large skillet. Add the veggies and let them cook for 5-7 minutes, or until slightly tender. While the veggies are cooking, whisk together the eggs, broth, rosemary, sage, thyme, salt, and pepper.
Grease your slow cooker. Add a layer of sourdough cubes to the slow cooker, followed by large spoonfuls of veggies, and then the rest of the bread and veggies. Pour the egg mixture over the top and stir. Cover, set the slow cooker to low and cook for 3-4 hours or cook on high for ~2-3 hours.
Check the stuffing periodically to see if it needs a dash of broth. I did not have issues with this, but every slow cooker is different. You can serve the finished stuffing right from the slow cooker, and can flip it to the "warm" setting while you're waiting to eat. Or you can transfer it to a baking dish, and put it in a preheated oven for a few minutes to make the top layer crispier, if desired.