You can cook with sencha, but treat it like a delicate green ingredient rather than a rugged spice. Brewed sencha can be used as a light poaching liquid for fish, mushrooms, rice, or noodles, and it works nicely in broths where you want fresh green bitterness and umami without heaviness.
Dry sencha leaves can also be ground lightly and used in salt blends, rice seasoning, shortbread, ice cream, or savory rubs. Keep heat gentle and amounts modest: scorched green tea gets bitter fast, and a little leaf can perfume a dish more elegantly than a lot.