Bring sauce to a simmer and cook, stirring occasionally, until slightly reduced, about 10-12 minutes.
Mix in spinach and cook until wilted, about 2 minutes. (An 8-oz. package is OK if you prefer a bit more spinach.)
Add beans and cook until heated through, about 3 minutes.
Split the sub rolls or bread lengthwise, toast under broiler or in toaster oven, and butter lightly. Ladle a generous portion of ragù over rolls and top with grated cheese and parsley.