Preheat oven to 400°. Peel parsnips, and cut into 2- to 3-inch-long pieces; cut each lengthwise into 1/3-inch-thick strips. Place in a lightly greased 15- x 10-inch jelly-roll pan; toss with pepper, 2 Tbsp. olive oil, and 1/2 tsp. kosher salt.
Bake at 400° for 25 minutes. Add green onions; toss. Bake 10 to 15 more minutes or until parsnips are tender and browned. Transfer to a serving platter.
Whisk together mint, next 3 ingredients, and remaining 1/2 tsp. salt until blended. Gradually add remaining 5 Tbsp. olive oil in a slow, steady stream, whisking until smooth. Spoon over vegetables. Serve immediately.
Brought to the table by cookbook authors Matt Lee and Ted Lee (The Lee Bros. Simple Fresh Southern cookbook).