1. Preheat oven to 400°F. In large pot of boiling water, cook carrots for 10 to 15 minutes or until fork-tender.
2. Keeping potatoes intact, thinly slice potatoes crosswise, stopping 1/4 inch from the bottom. Keeping carrots intact, thinly slice carrots crosswise and diagonally, stopping 1/4 inch from the bottom. Thinly slice garlic. Tuck slices of garlic and pieces of thyme between every other cut in potatoes and carrots.
3. Place potatoes and carrots on separate foil-lined rimmed baking sheets. Brush potatoes and carrots generously with olive oil; spread piece of butter over each potato and carrot. Season with salt and pepper. Fold foil over vegetables to form 2 packets, crimping to seal edges. Bake potatoes for 1 hour, then add carrots to oven; cook for additional 20 to 25 minutes or until vegetables are tender.
4. Remove foil packets from oven. Preheat broiler. Unwrap foil packets; broil vegetables for about 5 minutes or until browned with crisp edges.
5. Romesco Sauce: Meanwhile, in blender or food processor, combine roasted red peppers, almonds, sun-dried tomatoes, garlic, sherry vinegar, smoked paprika and salt until blended. Slowly drizzle in olive oil until mixture is emulsified.
6. Serve potatoes and carrots with Romesco sauce. Garnish with parsley.

Tips: 

• To easily cut the potatoes and carrots without slicing through the bottom, set them between 2 chopsticks or wooden spoons that will stop the knife from cutting all the way through.
• Serve with baked cod for a full meal.