So much of what we take for granted when we go out to eat Italian — or go out to eat, period — began with Babbo: Fine dining with a rock-and-roll soundtrack. Allegiance to both the most classic Italian recipes and the most local, seasonal ingredients. The once-daring embrace of offal. And let’s not forget wine by the quartino; pasta tastings; and all that evocative, goofily enticing menu language like “Mint Love Letters” and “Spicy Two Minute Calamari Sicilian Lifeguard Style” (is that really how Sicilian lifeguards do lunch?). When the joint opened in 1998, there wasn’t another Italian restaurant like it. Now, with co-owner Mario Batali in the process of divesting after sexual-assault allegations, the future of the restaurant is uncertain.