Sift the cake flour, almond flour, matcha, baking powder, and salt into a bowl and whisk to combine.
In a large bowl, beat eggs and sugar with a hand mixer on a medium speed until it has at least doubled in size, about 3 minutes. Add the melted butter and stir to combine.
Add the dry ingredients and gently fold until just about combined. Add the mini chocolate chips to the bowl and fold gently to combine. Cover the bowl and chill until cold, about 1- 3 hours.
About 15 minutes before you are ready to take the dough out of the fridge, preheat the oven to 350°F and line a baking sheet with a silicone mat.
Turn the biscotti dough out onto the prepared baking sheet and shape into a 12 inch log. I suggest wearing food safe gloves as the dough may be quite sticky. It also helps to use two cake scrapers to shape the dough.
Bake the log for 30 - 40 minutes, or until baked through. The biscotti is completely baked when the top springs back and a skewer comes out clean. Cool on the baking sheet for 15 minutes before carefully transferring to a cooling rack. Cool the log to room temperature.
When the log is cool, preheat the oven to 325°F. Slice into 1 inch cookies on a slight diagonal. Place the cookies upright on the lined baking sheet. Insulate the bottom of the baking sheet by placing it inside a second baking sheet of the same size. Bake for 40 minutes, rotating the pan halfway through. Place cookies on a cooling rack and cool completely.
Once cool, melt the chocolate over a double boiler, or in the microwave on half power. Pour the chocolate into a small piping bag. Snip the tip off and drizzle a bit of chocolate over each biscotti. Let them sit until the chocolate is completely set.
To store, place in an air tight container on the counter for up to 2 weeks. Serve with your favorite hot beverage.