Place thinly sliced zucchini rounds onto a paper towel and sprinkle with kosher salt to remove moisture. Let sit for 10+ minutes, then pat dry.
In a wide shallow pan, heat 1/2 cup olive oil over medium heat. Add the dried zucchini slices to the olive oil, making sure not to overcrowd the pan. Do this in batches if needed.
Fry zucchini until it begins to brown, then remove with a slotted spoon and place on a clean paper towel to remove excess oil. Once all zucchini is browned and removed, take a paper towel and wipe or dump out most of the olive oil. Retain around 2-3 tbsp.
To the still hot pan over medium heat, add 3 cups beans plus 1/2 cup heavy cream. Gentle simmer and fold in about half of the grated cheese. Add salt and pepper to taste.
Add the fried zucchini back in with the beans and gently stir to combine. Allow this to gently simmer for a few minutes until the sauce is the consistency of your liking. Remove from the heat and fold in the remaining half of grated cheese and 2-3 torn basil leaves.
Serve the beans hot, spritzing a small amount of lemon juice, any remaining grated cheese, and a few basil leaves for garnish.