make , definitely not cook. If you said you had cooked the tea (or coffee) it would mean that you had burnt it, stewed it, or otherwise ruined it. You cook food (including liquid foods like soup and sauces), but you make drinks.

May I add something?:) You can also say you "take your coffee with milk or without sugar". "Take" when describing the way you drink it.

Yeah cool thank you You better brew up a pot of coffee, it’s going to be a long night.

"brew" and "brew up" are also reasonably common