In a large saucepan, heat oil over medium. Add onion and garlic; season with salt and pepper. Cook, stirring occasionally, until onion begins to soften, 5 to 6 minutes. Add tomato paste, and cook, stirring, until onion is coated, about 30 seconds. Add collard greens, thyme, and red-pepper flakes. Cook, stirring, until collards start to wilt, 2 to 4 minutes.
Place 1/4 of beans in a bowl, and mash them with the back of a spoon (this will help thicken soup). Add all the beans to the pan, as well as tomatoes with juice and 4 cups water. Bring to a boil; reduce heat, cover and simmer, until collards are tender, 10 to 15 minutes. Season with salt and pepper; serve with grated Parmesan, if desired.