Preheat your oven to 400°F (204°C).
Scrub the potatoes and carrots and rinse under cold running water to remove any dirt; pat them dry with paper towels.
Chop the vegetables into medium-sized pieces, approximately 1 inch in size, for even cooking.
In a large mixing bowl, combine the cut potatoes and carrots with the smoked paprika, garlic powder, onion powder, thyme, a pinch of cayenne pepper (adjust to your heat preference), and season with salt and black pepper to taste.
Drizzle the vegetables with oil. Toss everything together until the potatoes and carrots are evenly coated with the seasoning and oil.
Spread the seasoned vegetables in a single layer onto a large baking sheet, ensuring they're not overcrowded to allow for even roasting.
Roast in the preheated oven for 30 to 35 minutes, or until the potatoes and carrots are tender and have a golden-brown exterior. Halfway through the baking time, give them a stir for more uniform browning.