Bring a medium pot of water to a boil over high heat. Add the potatoes and cook until just tender, about 8 to 10 minutes. Drain the potatoes and let cool. When cool, cut the potatoes in half.
Place a medium saute pan over medium heat. Add the butter, garlic, thyme and rosemary and let cook until the butter melts, about 2 minutes. Meanwhile, season the cut sides of the zucchini and potatoes with salt and pepper. Carefully place the zucchini and potatoes cut side down in the melted butter. Let them cook until golden brown, about 12 to 15 minutes.
Preheat the broiler. Line a baking sheet with foil. Place the browed zucchini and potatoes on the baking sheet cut side up. Sprinkle the tops with the Parmesan. Place in the broiler until the cheese is golden brown, about 4 minutes. Transfer to a plate and serve.
Recipe courtesy of Giada De Laurentiis