Slow-Cooker Bean and Barley Soup

1 cup dried multi-bean mix or Great Northern beans, picked over and rinsed

1/2 cup pearl barley

3 cloves garlic, smashed

2 medium carrots, roughly chopped

2 ribs celery, roughly chopped

1/2 medium onion, roughly chopped

1 bay leaf

Kosher salt

2 teaspoons dried Italian herb blend

Freshly ground black pepper

1/2 ounce dried porcini mushrooms, crumbled if large, optional

One 14-ounce can whole tomatoes, with juice

3 cups cleaned baby spinach leaves (about 3 ounces)

1/4 cup freshly grated Parmesan Balsamic vinegar, for drizzling

Extra-virgin olive oil, for drizzling