Using a Y-shaped vegetable peeler, cut zucchini lengthwise into very thin strips just until seeds are visible.
Toss zucchini ribbons with shallots and next 6 ingredients.
Serve immediately over arugula.
Squash Ribbons With Feta and Mint: Substitute yellow squash for zucchini. Proceed with recipe as directed.
Grilled Zucchini With Feta and Mint: Increase olive oil to 1/4 cup. Preheat grill to 350 to 400 (medium-high) heat.
Cut zucchini lengthwise into 1/4-inch-thick slices.
Brush with 2 Tbsp. olive oil. Grill zucchini, without grill lid, 2 to 3 minutes on each side or until tender. Proceed with recipe as directed in Step Prep: 20 min.; Grill: 6 min.