Preheat the oven to 325 degrees F, and grease an 8x8-inch pan with baking spray or butter. Optionally, line the pan with parchment paper, allowing two sides to hang over the edges (this will make the brownies easier to remove from the pan).
In a large heatproof bowl set over a pot of simmering water, stir the bittersweet chocolate and butter until evenly combined and smooth. Remove the pan from the heat.
Add the sugar and whisk vigorously until smooth, followed by the eggs, vanilla, and salt. Add in the flour and stir until smooth.
Pour the batter into the prepared pan. Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Allow the brownies to cool to room temperature.
In a stand mixer fitted with the paddle attachment, cream the butter on high speed until light and fluffy. Add the vanilla, then scrape down the sides. With the mixer on low speed, add the sugar, 2 teaspoons of matcha and salt. Mix until the dry ingredients have incorporated (add another 1/2 teaspoon matcha to amp up the flavor if desired). Scrape down the sides and turn the speed up to medium-high, allowing the frosting to mix for another 30-60 seconds, until light and smooth.
Carefully lift the brownies out of the pan and place them on a cutting board. Use a spatula to evenly frost the brownies. Cut into 16 squares and serve.