The Garden of Sinners
There's an inescapable entity when we talk about action anime nowadays: Kinoko Nasu, best known for the Fate/ series. The lavish adaptations of Fate/Stay Night by renowned studio Ufotable, who are attempting to cover all its branching stories, are just as popular as their take on the grittier prequel Fate/Zero. If you enjoy the central conceit of the series, which places famous heroes temporarily reborn as powerful magical servants in a competition for the Holy Grail, you can't go wrong with the recent Fate/Apocrypha either; rougher around the edges, but a more amusing take on it that totally disregards previously established rules, which also features some of the most impressive digital action animation in the medium altogether. My personal recommendation would be something much quieter, however: The Garden of Sinners' films. They follow Ryougi Shiki, who is blessed -- or perhaps cursed? -- with mystical eyes that allow her to observe the death of any being or object and slice their existence. Introspective at times, capable of effortlessly switching from effective horror to heartwarming romance, set in a somehow beautiful crumbling urban setting, and surprisingly compelling as an action piece despite the protagonist's ability being so absurdly strong. There's a lot to love in this series, which in many ways also served as a prototype for its more popular successors. Whether as an introduction to the so-called Nasuverse or for fans of Fate/, this is an excellent choice if you fancy action anime that isn't overly hectic.
Where to watch it: Stream on Crunchyroll, Amazon Prime.