In a large pot over medium-high heat, heat olive oil. Add the onion, garlic cloves and a pinch of salt. Cook, stirring occasionally, until the onion is translucent, about 5 minutes.
Reserve ¼ cup of beans for garnish. Add the tomatoes and their juices, the beans, broth, water, thyme sprigs, white pepper and ½ teaspoon salt. Bring to a boil, then reduce heat to medium and simmer 20 minutes.
Let cool for 5 minutes. Discard the thyme sprigs. Working in batches, transfer the soup to a blender and puree it until smooth. (Alternatively, use an immersion blender.) Season with salt and freshly cracked black pepper.
Drizzle olive oil over each bowl of soup and top with beans and a sprig of thyme.