Infusing in water
Tea can add tremendous flavor when added to cooking water for rice or pasta. Bring the water to a boil, then remove from heat. Add tea (slightly less than you would use to brew tea for drinking) and steep for the usual amount of time. Remove the tea (strain or remove tea pyramid.) Then cook pasta or rice as usual using this water. You can use the same method to create a savory cooking liquid for shellfish.
You can also create a tea concentrate for braising or adding to sauces.
Infusing with other liquids
This method allows you to add tea flavors to ice creams, ganache, and soups with a cream base. You can also infuse vinegar and juice.
In hot liquids scald cream as called for in the recipe. Add tea leaves and let steep. Strain when infusion reaches required strength. (The cream reduces the bitterness usually caused by a long steeping time so taste for doneness.) Use this method for:
In cold liquids: add the tea leaves to the liquid and let sit until they reach the desired strength. This can be used to infuse vinegar or alcohol.
Steep the tea in water as you would to make a cup of tea to drink, but add more leaf. Add other aromatics, flavorings, and oils. Marinate poultry or other meat in the mixture. Some options could include:
Adding Leaves for Flavoring
Use a mortar and pestle or a spice grinder to grind to the tea leaves to a powder. These ground leaves can be used in spice rubs and baked goods. Matcha can be used in this way as well without the need for grinding. Suggestions for this technique include:
Curing, Brining, and Pickling
Whole leaves or tea concentrate can be added to brining and pickling liquids. Another interesting thing to try is to make gravlax by curing salmon with a combination of salt, sugar, and tea leaves.
Wet tea leaves and use as you would use mesquite chips in a grill box. Souchong leaves work well for this purpose. You can also smoke in a wok using equal parts uncooked rice and dry leaves along with aromatics and flavorings like sugar, black pepper, cinnamon, apple slices, or nuts. Black tea is wonderful to use for smoking chicken or salmon.