Place shredded zucchini in a colander. Sprinkle with one teaspoon salt. Let drain for 10 minutes.
Heat oven to 425. Line baking sheet with parchment.
Whisk flour, baking powder, baking soda and salt in large bowl. Cut cold butter into flour mixture using a fork or pastry blender until crumbly.
Pour buttermilk into <g class="gr_ gr_88 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar only-ins replaceWithoutSep" id="88" data-gr-id="88">flour</g> mixture and stir with rubber spatula until just incorporated. Stir in shredded zucchini, cheese, <g class="gr_ gr_89 gr-alert gr_gramm gr_inline_cards gr_run_anim Punctuation only-ins replaceWithoutSep" id="89" data-gr-id="89">basil</g> and rosemary.
Use a greased 1/4 cup dry measuring cup. Scoop out <g class="gr_ gr_87 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar only-ins replaceWithoutSep" id="87" data-gr-id="87">level</g> amount and drop onto parchment. Leave 1 - 1/2 inches between biscuits.
Bake for about 20-25 minutes or until tops <g class="gr_ gr_86 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace" id="86" data-gr-id="86">are</g> golden brown and crisp.
Brush with melted butter, if desired. Let cool 5 minutes before serving.