Combine the softened butter and sugar in a mixing bowl and beat with a whisk until the mixture is light and fluffy, about 2-3 minutes.
Add the finely grated ginger and mix until evenly incorporated, releasing a warm spicy aroma.
Beat in the egg until the mixture is smooth and slightly thickened.
Pour in the cooled, steeped herbal tea and stir until just combined, infusing the dough with floral notes.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry mixture to the wet ingredients, folding gently until a sticky dough forms.
Gather the dough into a ball, wrap it in plastic wrap, and chill in the refrigerator for at least 30 minutes to relax the gluten.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Remove the chilled dough from the fridge and roll it out on a lightly floured surface to about 1/4 inch thickness.
Use a cookie cutter or glass to cut out rounds and place them about 1 inch apart on the prepared baking sheet.
Bake in the preheated oven until the edges are golden brown, about 10 minutes.
Let the cookies cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely. Enjoy their crispy edges and chewy centers, infused with floral tea and spicy ginger flavor.