Preheat the oven to 350°F (180°C) and line two baking sheets with parchment paper.
In a bowl, whisk together the bread flour, baking soda, salt, and matcha powder until well combined.
In a stand mixer fitted with a paddle attachment (or use a hand mixer and a bowl), cream together the butter and sugar until paste-like in consistency.
Add the egg and vanilla extract to the butter-sugar mixture and mix until fully incorporated.
Gradually add the dry ingredients mixture to the butter-sugar mixture and mix until just combined, being careful not to overmix.
Form 16 even dough balls using your hands or a cookie scoop and place them on the prepared baking sheets, spacing the cookies about 2 inches apart.
Bake the cookies in batches for 10-12 minutes or until the edges are lightly golden, the cookies are puffy, and they have finished spreading.
Remove the cookies from the oven and drop the baking sheet a couple of times on a flat surface to deflate the cookies. Let them cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Place ⅔ of the chocolate in a microwave-safe bowl. Heat in short increments, mixing well in between, until 85% of the chocolate has melted.
Fold the rest of the chocolate and leave it to sit on the kitchen counter for 1 minute. Then, mix until all chocolate has melted and the mixture looks homogenous.
Dip approximately half of each cookie in the chocolate and shake off the excess. Place the cookies on the parchment paper to set.