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Pegeen is a trusted home cook.
No, parchment paper won't prevent browning. You might want to flip the carrots once with a spatula halfway through the cooking time. Before you put them in the oven, you might want to toss them a tablespoon or two of light olive oil, salt and pepper.
As Pegeen says, but I like to toss the vegetables with a bit of tomato paste too. A tablespoon for a servings size for four is plenty. The paste caramalizes when in the oven and helps give a nice crispy outside to the veg. Don't be afraid to use a higher heat than you are accustomed too - perhaps 400+F - BUT, watch closely.
Your vegetables will brown perfectly on parchment. Parchment paper is my key to great oven fries, perfect roasted brussel sprouts, and beautiful roasted carrots. The beauty of parchment is that virtually nothing sticks to it, yet it miracuously acts as a conduit for your metallic sheet pan. Every cook should have this tip in their repertoire, particularly for roasting potatoes. I purchase pre-cut sheets from a baking store here in nyc. Cleanup is a breeze also. I forgot-I also roast and broil fish on a parchment lined pan, aluminum foil always sticks, and their is zero need to use any cooking spray with parchment.
Shuna is a pastry chef in New York City and author of the acclaimed blog Eggbeater.
The only thing I will add to this is: Caution. High heat roasting (400F+) could roast the parchment paper too. In a convection oven this is a bit "dangerous," as the paper alights and becomes cinder & ash that gets in your food. Parchment paper is not 100% paper/tree pulp, so it should not be ingested.
Interesting point on the potential for parchment to burn. My box states 500 degrees as the max temperature, Im sure other brands wll be different. Another reason to use the ready cut sheets-there is no "overhang" which would more likely catch fire. Good safety point here on parchment!