Melt the butter in a saucepan over medium heat. Add the garlic, the dry rub, and lemon zest. Cook, stirring continuously for about 3 minutes. Remove from the heat and set aside to cool.
Wash and dry the zucchini. Use a mandolin to cut thin strips lengthwise about 1/8 inch thick.
Lay the slices out and brush with the butter mixture making sure to coat each piece.
Fold the zucchini into an accordion shape, like ribbon candy, and thread onto metal or wooden skewers.
Add the skewers to the grill and baste with remaining butter. Grill 1-2 minutes per side on all for sides until golden brown with singed edges.