Heat oven to 450°F Line baking sheet with parchment paper. Combine zucchini and 1/4 tsp of the salt in a small bowl; let stand 20 minutes. Discard excess liquid. Place zucchini in strainer; press on zucchini to drain any additional liquid. Combine zucchini, cheese, green onions and 1 Tbsp of the flour in medium bowl.
Whisk remaining 2 cups flour, baking powder and remaining 1/4 tsp salt in medium bowl. With pastry blender or two knives, cut in butter until mixture resembles small peas. Stir in zucchini mixture. Stir in milk just until soft dough forms.
Drop dough by tablespoonfuls onto baking sheet. Bake 10- 13 minutes or until light brown on top and bottom. Serve warm.