Place a rack in middle of oven; preheat to 375°. Melt ½ cup (1 stick) unsalted butter in a small skillet over medium-low heat (don’t let it boil). Stir in 1 Tbsp. black tea leaves (from about 3 bags), then pour into a medium bowl, scraping pan to get all the bits of tea. Let butter mixture sit until barely warm, about 10 minutes.

Add 1 large egg, ¾ cup (150 g) granulated sugar, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 1 tsp. vanilla bean paste or vanilla extract to butter mixture and mix vigorously with a rubber spatula until smooth. Add ¼ tsp. baking powder, ¼ tsp. baking soda, and ¼ tsp. ground cinnamon and mix again to combine. Add 1½ cups (187 g) all-purpose flour and mix until no dry streaks remain, making sure to scrape sides and bottom of bowl.

Divide dough into 32 portions (2 tsp. or 14 g each; easiest way to do this is to divide dough into quarters, then divide each quarter into 8 pieces). Roll each portion into a ball. Divide balls between 2 parchment-lined baking sheets, spacing evenly apart.

Working with 1 baking sheet at a time, bake cookies until puffed and dry to the touch, 6–8 minutes. Let cool on baking sheets. Do Ahead: Cookies can be baked 5 days ahead. Store airtight at room temperature.

Using an electric mixer, starting on low speed and moving to medium, beat ¾ cup (83 g) powdered sugar, sifted, 6 Tbsp. unsalted butter, room temperature, 1 tsp. (packed) finely grated peeled ginger, ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, ½ tsp. ground cardamom, and ½ tsp. vanilla bean paste or vanilla extract in a medium bowl until smooth and fluffy, about 3 minutes (or, you can use a whisk).

Transfer filling to a pastry bag fitted with a medium round tip. Turn half of the cookies over and pipe kisses of filling onto flat sides, dividing evenly (alternatively, you can dollop a heaping 1 tsp. filling onto each one). Place remaining cookies, right side up, on top, gently pressing until filling spreads almost to edges of cookies. Chill creme pies 10 minutes to allow filling to firm slightly before serving. Do Ahead: Creme pies can be assembled 2 days ahead. Transfer to an airtight container and chill. Bring to room temperature before serving.