Cut room temperature butter into chunks and add to your food processor along with sugar.
In a small matcha bowl, sift matcha powder by pushing it through the sift with a spoon. Add hot water and use the bamboo whisk to incorporate the matcha into the water, whisking in an "M" or "W" shaped motion. The mixture should be glossy and thick, with no clumps remaining.
Pour the thick matcha mixture into the food processor and process on high until fully incorporated. You may need to pause and scrape the sides down using a spatula in between pulses.
Once smooth, transfer to an airtight container to store in the refrigerator for up to one week, or enjoy immediately!