Preheat oven to 350°. On a baking sheet, toss bread, oil, oregano, garlic powder, and a large pinch of salt. Spread in an even layer.
Bake croutons, shaking pan halfway through, until golden and crispy, 15 to 18 minutes.
In a large pot over medium heat, heat oil. Add onion and cook, stirring, until softened, about 8 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute more. Add tomato paste and cook, stirring, until onions are coated and paste slightly darkens, about 2 minutes.
Stir in tomatoes, broth, and 1 cup beans until combined. Add oregano and red pepper flakes; season with salt and black pepper. Bring to a boil, then reduce heat to medium-low and bring to a simmer. Cook, stirring occasionally, until slightly reduced and flavors have melded, about 20 minutes.
Remove pot from heat and carefully puree with an immersion blender until smooth. Alternatively, transfer soup to a standard blender and blend, stopping to allow steam to escape very carefully every 10 seconds, until smooth.
Return soup to medium-low heat. Add spinach, Parmesan, cream, and remaining beans. Bring to a simmer and cook, stirring occasionally, until spinach is wilted and cheese is melted and incorporated, about 10 minutes more.
Divide soup among bowls. Top with croutons and more Parmesan.
