Special equipment: a pastry brush
Line a baking sheet with parchment paper and set aside. Combine the flour, sugar, matcha, baking powder and 1 teaspoon salt in a large bowl and whisk until evenly combined. Add the chilled butter and rub it into the flour with your fingers until it resembles a coarse meal. Combine the chives and tarragon in a small bowl, then scoop out and reserve 1 tablespoon of the herbs in another bowl. Sprinkle the remaining herbs in the flour mixture and toss until evenly incorporated.
Form a well in the center of the flour mixture, then pour in the cream. Using a fork, stir until the dough just comes together (it will be wet and sticky). Transfer the dough to well-floured work surface and, using well-floured hands, pat into a 9-by-6-inch rectangle, about 3/4-inch thick. Using a large knife, halve the rectangle lengthwise, then cut crosswise into thirds, creating six 3-by-3-inch squares. Halve each square diagonally to create 12 triangles, then transfer all the triangles to the prepared baking sheet and space apart evenly. Freeze for 1 hour to firm up.
Meanwhile, in a small bowl, add the room temperature butter, pepper and the remaining 1/4 teaspoon salt. Add the reserved herbs and stir to combine. Set aside.
Preheat the oven to 400 degrees F.
Using a pastry brush, dust off any excess flour attached to the scones, then brush the tops of the scones with cream. Bake the scones until puffed and golden brown on top, 20 to 25 minutes. Transfer the scones to a wire rack and let cool for 10 minutes, then serve warm with the herb butter on the side.
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