Set oven to 425°F (220°C). Place the empty baking sheet on the middle rack while the oven preheats, about 15 minutes.
Peel carrots and cut into ¾-inch diagonal slices. Halve baby potatoes or cut Yukon Golds into 1 to 1.25-inch chunks. Pat all pieces dry with paper towels.
Add vegetables to a large bowl. Drizzle with olive oil and toss. Add garlic powder, thyme, rosemary, paprika, salt, and pepper. Toss until every piece is evenly coated.
Remove the preheated sheet from the oven. Spread vegetables in a single layer with space between pieces. Place potato chunks cut-side down. Use two pans if the pan is crowded.
Roast undisturbed for 15 minutes. Flip the vegetables, then roast for another 12 to 15 minutes until edges are golden brown and potatoes are fork-tender.
Remove from oven. Squeeze lemon juice or drizzle balsamic over the hot vegetables. Scatter fresh parsley and serve immediately.