With Food Network’s Into the Fire already to his credit, filmmaker Joseph Levy seems appropriately at ease infiltrating the communities that spring up within and around professional kitchens. He also produced the short film George Lucas in Love, and could be said to enjoy probing presumably alien worlds for familiar down-home comforts. Levy’s likable doc Spinning Plates, which has taken audience awards at several film festivals, looks fondly behind the scenes at three very different eateries: a 150-year-old family restaurant in Iowa which burned down twice; a chic Chicago molecular-gastronomy hotspot whose famous chef nearly succumbed to tongue cancer; and a no-frills Mexican joint in Tucson whose humble proprietors just hope to stay afloat. Each has its own token of ambition — be it regionally superlative fried chicken, a third Michelin star, or the security of a little girl’s future — and, accordingly, each has its own philosophy about the nurturing power of food, usually at least in part a function of endurance. Levy’s structure raises some questions that will be naggingly familiar to viewers of similar multi-part documentary portraits: Why three, and why these three in particular? And, as if encouraged by the movie’s marginally treacly score, his subjects do tend to speak in platitudes. But there’s something truly delectable about how they’ve all let him in on their undeniably nourishing life’s work.