Heat the olive oil in a large pot over medium-high heat, and sauté the onion until it starts to soften, about 5 minutes.
Add in the garlic and stir briefly, just until fragrant, about 1 more minute.
Add the drained white beans to a blender, along with the water and cashews (if using). Blend until very smooth, then immediately add it to the pot, so the garlic won't burn.
Add in the broccoli and shredded carrot, along with 2 teaspoons of salt and a 1/2 teaspoon of ground black pepper. Bring the liquid to a boil.
Once the liquid is boiling, lower the heat and cover with a lid. Let the soup gently simmer for 15 to 20 minutes, or until the broccoli is very tender.
Transfer roughly 3 cups of the soup to a blender, making sure to grab any large pieces of broccoli, so there won't be large chunks in the soup. Blend briefly, pulsing the broccoli into smaller pieces, but not blending until it's totally pureed.
Return the blended soup to the pot, then add in the shredded cheese. Stir briefly, just until the cheese has melted, then adjust any seasoning to taste.
Serve warm with any extra toppings you love, like extra cheese or a pinch of nutmeg. Leftover soup can be stored in an airtight container in the fridge for up to 5 days.