Heat a Dutch oven over medium-high heat. Add cooking oil and then garlic, chard stems, tomato paste, balsamic vinegar, soy sauce, Italian seasonings, basil, and black pepper to heated oil. Saute for ~2 minutes, letting the flavors caramelize together.
Add carrots, celery, diced tomatoes, broth, and parmesan rind. Bring to a boil and then add mushrooms. Simmer uncovered for 10 to 15 minutes, until carrots and celery are tender.
Fold in beans and chard leaves.
Fish out parmesan rind, and season to taste with salt and pepper. Divide into bowls and sprinkle with more parmesan. Enjoy with crusty bread if using.