White Bean Ragout with Toast

Name: White Bean Ragout with Toast
Ingredients: 3 medium onions, chopped; 1 red bell pepper, chopped; 1/2 cup extra-virgin olive oil plus more; Kosher salt; freshly ground pepper; 4 garlic cloves, 3 finely grated, 1 halved; 2 teaspoons tomato paste; 4-6 1-thick slices grilled or toasted ciabatta; 8-10 tablespoons finely grated Parmesan, divided; 2 15-ounce cans cannellini (white kidney) beans, rinsed and drained; 4 cups vegetable broth, divided; 1 cup cherry tomatoes, halved; 2 tablespoons chopped flat-leaf parsley