Place potatoes and sage in 15- x 10-inch jelly-roll pan. Drizzle 1/4 cup olive oil over mixture; toss gently.
Bake at 450°, stirring every 15 minutes, for 35 to 40 minutes or until potatoes are tender and browned. Cool. Cut potatoes in half; sprinkle with 1 teaspoon salt and 1/2 teaspoon pepper. Place potatoes in a large serving bowl. Crumble roasted sage leaves over potatoes.
Whisk together remaining 1/4 cup oil, red wine vinegar, 1/4 teaspoon salt, 1/4 teaspoon pepper, shallots, and thyme; drizzle over potato mixture, Toss gently. Top with fresh sage leaves and thyme sprigs. Serve with Aí oli, if desired.