Step 1: Prepare the Vegetables

1. Preheat your oven to 400°F (200°C).
2. Peel and thinly slice the red beets, golden beets, and sweet potatoes. Use a mandoline slicer for even, thin slices.
3. Place the sliced vegetables in a large bowl. Drizzle with olive oil, then season with salt, black pepper, dried thyme, and garlic powder. Toss well to coat the slices evenly.

Step 2: Layer the Vegetables

1. Lightly grease a baking dish (9×13 inches or similar size).
2. Start by arranging a single layer of sweet potato slices, followed by a layer of red beets, and then a layer of golden beets.
3. Repeat the process until all the vegetable slices are used up, making sure the layers are compact and evenly distributed.

Step 3: Bake the Vegetables

1. Cover the baking dish with aluminum foil and place it in the preheated oven.
2. Bake for 40 minutes, or until the vegetables are tender.
3. Remove the foil and bake for an additional 10-15 minutes to achieve a slight crispiness on top.

Step 4: Make the Pistachio Pesto

1. While the vegetables are baking, prepare the pistachio pesto. In a food processor, combine basil leaves, shelled pistachios, grated Parmesan cheese, garlic cloves, lemon juice, salt, and pepper.
2. Pulse the mixture until finely chopped.
3. With the food processor running, slowly drizzle in the olive oil until the pesto reaches a smooth, creamy consistency. Taste and adjust seasoning as needed.

Step 5: Assemble the Dish

1. Once the vegetables are done baking, remove the dish from the oven.
2. Tear the burrata balls into pieces and distribute them evenly over the baked vegetable layers.
3. Spoon generous dollops of pistachio pesto over the burrata.