Preheat the oven to 425°F.
On a large rimmed sheet pan, toss the potatoes and carrots with 2 tablespoons of the olive oil, ½ teaspoon of the salt, ¼ teaspoon of the pepper, the garlic powder and the Italian seasoning. Spread in a single layer.
Roast for 15 minutes.
Meanwhile, toss the broccoli and bell peppers in a bowl with the remaining 1 tablespoon oil, ½ teaspoon salt and ¼ teaspoon pepper.
Take the pan out of the oven, stir the potatoes and carrots, and add the broccoli and peppers. Spread everything out again.
Roast for 15–20 minutes more, until the potatoes are tender when pierced with a fork and the vegetables are golden at the edges.
Taste, add more salt if needed and serve warm.