Preheat the oven to 425 degrees F.
Prepare the carrots and parsnips for roasting. Scrub them clean with a vegetable brush (or your hands) and trim off the tops and ends. Slice each one crosswise on an angle into ½-inch coins. For any that have large tops and skinny bottoms, slice the wider coins you get from the top in half or quarters. Cut longer pieces from the skinny bottoms. Overall, you want the vegetables to be approximately the same size.
In a measuring cup, combine the olive oil, runny honey, thyme leaves, chopped rosemary, salt, and pepper. Whisk until smooth.
Put the prepared vegetables in a 12-inch cast iron skillet. Pour the honey glaze on top and stir well so the vegetables are fully coated. Even after the vegetables are coated, there should be a puddle of the glaze in the bottom of the pan. It won't be a very large amount but it should cover the pan. The vegetables will be on top of each other. This is OK and intended, as they will cook down.
Place the skillet on the middle rack of the oven and roast for 35 to up to 50 minutes, until the vegetables are caramelized on the outside to your liking and fork-tender. Stir the vegetables at least once and preferably twice during the cooking time. This will promote even cooking. I prefer to cook mine for a full 50 minutes.
When you're ready to serve the vegetables, keep them right in the skillet (just warn your guests that it will be hot!) so they keep their warmth. Top them with pats of butter, some more fresh herbs (if desired), flaky sea salt, and another drizzle of honey (all optional...they're great as is too!). Enjoy!
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