Whisk flour, baking soda, salt, and 2 tablespoons of matcha in a medium bowl. Using an electric mixer on medium-high speed, beat the butter, brown sugar, and honey in a medium bowl until light and fluffy, about 4 minutes. Add the egg, egg yolk, and lemon zest, and mix until very pale, about 4 minutes.
Reduce mixer speed to low and, with motor running, add the flour mixture; mix until no dry spots remain. Using a wooden spoon or rubber spatula, mix in the white chocolate.
Wrap the dough in plastic and chill at least 2 hours and up to 5 days. If chilling more than a few hours, let the dough sit at room temperature for 1 hour to soften before scooping and baking.
Whisk the 1/2 cup granulated sugar and remaining 1 1/2 teaspoons matcha in a small bowl; set aside.
Preheat the oven to 350° F. Scoop the dough by the scant tablespoonful onto 2 parchment-lined baking sheets, spacing each about 1 inch apart.
Bake the cookies, rotating the baking sheet halfway through, until bottoms and edges are barely golden and cooked (top will no longer look wet), 8 to 10 minutes.
Immediately -- but gently -- toss cookies in the reserved matcha sugar and place on wire racks; let cool. Store cookies airtight at room temperature for up to 2 days.