FLCL

In the city of Mabase, a seemingly ordinary young boy named Naota Nandaba's life takes an unexpected turn when a mysterious woman on a Vespa motorcycle crashes into him. As a result, he discovers a strange, growing protrusion on his forehead and finds himself caught up in a series of bizarre events involving robots and interdimensional beings. With the help of his new housekeeper, Haruko, who appears to be hiding secrets of her own, Naota must navigate this strange new world and confront his own buried emotions to unlock the secrets of his mysterious power. Will he be able to control his newfound abilities and uncover the truth behind them, or will they consume him and destroy everything he holds dear?

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Some TV shows that have similar genres and were produced around the same time as FLCL include Rick and Morty, The Testament of Sister New Devil, LEGO Monkie Kid, Full Metal Panic! The Second Raid, Future Boy Conan (Japanese Language Version), Wise Man's Grandchild.