1. Preheat oven to 400°. Bring a large pot of water to a boil over high heat and add potatoes. Boil potatoes until barely tender when pricked with a fork, about 5 minutes, then drain them completely and spread in a single layer on a large rimmed baking sheet. Add carrots, drizzle vegetables with olive oil, season generously with salt and pepper, and gently toss to coat evenly. Bake, stirring occasionally, until potatoes are golden brown, about 20 minutes.
2. Transfer vegetables to a large bowl and add thyme and butter; gently toss to coat evenly. Serve warm or at room temperature.
Note: Nutritional analysis is per serving.
Fingerling potatoes, available at large grocery stores and farmers' markets, would be a nice substitute for the Yukon Golds. You can make this dish up to 5 hours ahead, then reheat in a 350° oven just before serving.