Preheat oven to 350°. Beat butter, sugar, salt, and vanilla in a large bowl with a mixer until smooth. In another bowl, stir together flour, cinnamon, ginger, fennel, cardamom, and tea. Add to butter mixture and beat on low speed until blended. Stir in chocolate chips.
Line 2 baking sheets with parchment paper. Set 1-tbsp. balls of dough 1 in. apart on sheets and flatten slightly with a floured glass.
Bake until cookies are light golden on undersides, 15 to 18 minutes, switching pan positions halfway through baking. Transfer to racks to cool.
*Grind in a clean coffee grinder or in a mortar.
Make ahead: Up to 3 days, stored airtight.
Note: Nutritional analysis is per cookie.