Heat 1 tbsp. olive oil in a large pot over medium heat. Add onion and garlic; cook until transparent, about 5 minutes. Add carrots and celery and cook, stirring often, 5 minutes. Stir in broth and beans, then bring to a boil. Reduce heat, cover, and simmer about 15 minutes. Add tomatoes and chard and simmer another 15 minutes, covered.
Meanwhile, preheat oven to 350°. Lay bread pieces on a rimmed baking sheet in a single layer. Drizzle with remaining 2 tbsp. olive oil and sprinkle with salt and pepper. Toast in oven until slightly golden, about 10 minutes. Set croutons aside.
Just before serving, add basil and cilantro and season to taste with salt and pepper.
Divide soup among serving bowls and top each with a few warm croutons. Grate parmesan directly over soup if you like.
*Muir Glen canned tomatoes are exceptionally flavorful and somehow don't taste as canned as other brands.