Slice the zucchini into long ribbons 1/16-inch thick using a mandoline slicer.
Add the butter and oil to a large saute pan over medium-high heat. Add the shallots then the zucchini in two batches and toss through the hot butter and oil, using tongs, until soft, a good 4 to 5 minutes. Add the basil, parsley and lemon zest at the very end. Season the zucchini with salt and pepper and stir. Transfer to a serving bowl.