Place the basil and boiling water in a bowl and steep for 10 minutes. Strain out the basil and stir in the honey. Place the matcha in a small bowl. Add in 1/4 cup of the basil water and mix with a bamboo whisk until the matcha is smooth and clump free.
Add the matcha back into the basil water along with the lemon juice and 2 cups of cold water. Stir to combine, pour over ice, and serve.