Preheat the oven: Begin by preheating your oven to 400°F (200°C). This ensures an even roast.
Toss the sweet potatoes: In a large mixing bowl, combine the diced sweet potatoes (2 large), 2 tablespoons of olive oil (from the total 3 tablespoons), 1/2 teaspoon of salt (from the total 1 teaspoon), 1/4 teaspoon black pepper (from the total 1/2 teaspoon), 1/2 teaspoon garlic powder (from the total 1 teaspoon), and 1/2 teaspoon paprika (from the total 1 teaspoon). Toss everything well to coat the sweet potatoes evenly.
Roast the sweet potatoes: Spread the seasoned sweet potatoes in a single layer on a baking sheet lined with parchment paper. Roast in the preheated oven for 20 minutes or until they are tender and slightly caramelized, stirring halfway through for even cooking.
Prepare the broccoli: While the sweet potatoes are roasting, take the broccoli florets (1 large head) and toss them in a mixing bowl with the remaining 1 tablespoon of olive oil, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Ensure they are well coated.
Add broccoli and pecans: After the sweet potatoes have roasted for 20 minutes, remove the baking sheet from the oven. Add the seasoned broccoli and chopped pecans (1 cup) to the baking sheet. Toss everything together to combine.
Finish roasting: Return the baking sheet to the oven and roast everything together for an additional 15-20 minutes, or until the broccoli is tender and the pecans are toasted. Keep an eye on the pecans to prevent burning.
Serve: Once everything is perfectly roasted, remove it from the oven, and let it cool slightly before serving. Enjoy this vibrant dish warm, as part of your holiday spread.