Heat 2 tablespoons olive oil in a large saucepan over medium-high heat until shimmering. Add garlic, onions, oregano, and red pepper flakes. Cook, stirring frequently until onions are softened but not browned, about 4 minutes. Add bread and tomatoes. Roughly mash tomatoes with a whisk or a potato masher. Add 2 cups water. Bring to a boil over high heat, then reduce to a simmer. Cook for 5 minutes.

Transfer half of the soup to the jar of a blender. Blend soup, starting at low speed and gradually increasing to high. With blender running on high, gradually trickle in half of remaining olive oil. Season soup to taste with salt and pepper. Transfer to a large bowl and repeat with remaining half of soup and olive oil. Ladle into individual serving bowls, top with minced herbs, drizzle with more olive oil, and serve with toast or grilled cheese.