Preheat your oven to 375°F. While it heats, prepare all your vegetables: cut the carrots into 2-inch pieces, cube the potatoes and sweet potato into 1-inch pieces, halve the brussels sprouts, and cut the red onion into 1-inch wedges. Having everything prepped and ready before you start cooking ensures a smooth workflow and prevents any vegetables from sitting around and oxidizing.

In a small bowl, whisk together the olive oil, 2 tablespoons balsamic vinegar, brown sugar, salt, and black pepper until the sugar dissolves completely. Reserve 1-2 tablespoons of this dressing in a separate small bowl for finishing. Add the prepared vegetables to a large baking sheet and pour the majority of the dressing over them, tossing well with your hands or two spoons to ensure every piece gets coated. I find that tossing by hand helps you feel when everything is evenly dressed, preventing some pieces from getting too much oil while others dry out.

Spread the coated vegetables in a single layer on the baking sheet, arranging them so they have contact with the hot pan—this direct contact creates caramelization and deeper flavor. Roast for 30-45 minutes, stirring halfway through the cooking time, until the vegetables are tender and the edges are golden brown and slightly charred. The potatoes and carrots will take the longest to cook, so check them for doneness before removing the pan from the oven.

Remove the roasted vegetables from the oven and let them cool for a few minutes—this allows the residual heat to gently finish cooking any pieces that need it. Drizzle the reserved dressing over the warm vegetables and toss gently to distribute it. Crumble the feta cheese over the top and give everything one final gentle toss. I like to finish with a light drizzle of additional balsamic vinegar right before serving for a bright, tangy note that cuts through the richness of the cheese and oil.