Step 1: Prepare the Sweet Potatoes

1. Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper or lightly grease it.
2. Prick each sweet potato a few times with a fork to allow steam to escape.
3. Rub each potato with 1/2 tablespoon of olive oil, then season with salt and pepper.
4. Place the potatoes on the prepared baking sheet and bake for 45-60 minutes or until they are soft and fork-tender.

Step 2: Roast the Carrots

1. While the sweet potatoes bake, toss the carrot slices in a bowl with olive oil, salt, pepper, and smoked paprika (if using).
2. Spread the carrots on a separate baking sheet lined with parchment paper.
3. Roast for 20-25 minutes, stirring halfway through, until they are tender and slightly caramelized.

Step 3: Make the Thyme Walnut Pesto

1. In a food processor, combine the toasted walnuts, basil leaves, thyme leaves, Parmesan cheese, and minced garlic.
2. Pulse a few times to break down the ingredients.
3. Slowly drizzle in the olive oil while the processor is running until the mixture reaches a smooth consistency. Add more olive oil if needed for a thinner pesto.
4. Season with salt, pepper, and lemon juice. Pulse a few more times to blend, then set aside.

Step 4: Assemble the Stuffed Sweet Potatoes

1. Once the sweet potatoes are done, let them cool slightly, then slice each one lengthwise to create a small opening.
2. Use a fork to gently fluff up the insides of the sweet potatoes, creating a small pocket for the filling.
3. Fill each sweet potato with torn pieces of burrata cheese, allowing it to melt slightly from the warmth of the potato.

Step 5: Add Roasted Carrots and Top with Pesto

1. Top each stuffed sweet potato with an even portion of the roasted carrots.
2. Drizzle each sweet potato generously with the thyme walnut pesto, ensuring each bite has a bit of the earthy, aromatic flavor.