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Place a rack in the bottom of your oven and preheat oven to 400 degrees F. Slice all vegetables into chunks roughly 1 1/2 inches wide. The more similar the size of the vegetable pieces, the more evenly they will roast.
Place cut vegetables into a large mixing bowl. Add 3 tbsp olive oil, fresh thyme leaves, ground cumin, kosher salt, and black pepper. Stir until all vegetables are evenly coated with oil, spice and herbs.
Brush large rimmed baking sheet with remaining 1 tbsp olive oil. Spread the vegetables out evenly on the baking sheet. Place the rosemary sprigs on top of the vegetables, evenly spaces across the sheet.
Roast the vegetables in the oven for 15 minutes. Stir the vegetables, bringing the chunks from the outside towards the center and the chunks in the center out towards the edges. Return baking sheet to oven and continue to roast until the largest chunks are tender and the edges are starting to turn golden/dark, another 15-25 minutes.
Remove the roasted rosemary sprigs and stir the vegetables (some leaves of rosemary will remain, this is good). Season with additional salt and pepper to taste, if desired. Vegetables can be served warm or at room temperature.