Heat olive oil in a large skillet over medium heat. add the onion and potatoes, cooking until the onion softens and the potatoes start to brown, about 8 minutes.
Stir in the garlic and cook for 1-2 minutes until fragrant. season with salt and pepper.
Pour in the broth and bring the mixture to a boil. reduce to a simmer and cook until the potatoes are fork-tender, about 10-12 minutes.
Add the broccoli and cook until just tender, about 5-7 minutes. toss in the spinach and cook for 30 seconds to 1 minute, just until wilted.
Carefully transfer the mixture to a blender, adding the shredded cheese and a splash of half and half. blend on high until smooth and creamy.
Return the blended mixture to the skillet over low heat. stir in the butter beans and cook until warmed through.
Drizzle with olive oil, sprinkle with more shredded cheddar and black pepper, and serve with toasted bread for dipping.
