Carrots and beets are particularly good when roasted as it brings out their natural sugars. The best advice I can give you is about flavoring them. A few smashed garlic cloves, a woody herb like rosemary, thyme, sage or bay, and a splash of vinegar, or squeezed lemon or orange juice, can accentuate their natural flavor.
Preheat the oven to 425 degrees F. Put the carrots into a large pot and the beets into another, and add enough water to cover them. Season with salt and bring to a boil. Cook for 15 to 20 minutes until just tender, then drain and place in separate bowls. Peel the beets, and cut any larger carrots and beets in half or into quarters. Smaller ones can stay whole.
Now add the flavorings while the vegetables are still hot. Toss the carrots with half the smashed garlic and a glug of olive oil, then lightly season. Add the orange juice and the thyme leaves and toss again. Mix the beets with the rest of the garlic, the rosemary, balsamic vinegar and salt and pepper. You can now put the vegetables either into separate ovenproof dishes, or together on a large roasting pan with the carrots in 1 half of the pan and the beets in the other. Place in the middle of the preheated oven and roast for around 1/2 hour or until golden.
While the carrots and beets are cooking, lay the chops on a board and score through the skin and the streaky-looking part of the meat. This will give you lovely crackling.
Firmly press a sage leaf onto the eye meat on both sides of each chop. Season with salt and pepper.
When the vegetables start to color, heat a large ovenproof frying pan or small roasting pan on the burner, add a good glug of olive oil and put in the chops. As soon as you've got nice color on 1 side, turn the chops over and place the pan in the oven for 10 minutes, or until the chops are crisp on the outside and just cooked through and juicy in the middle. Remove the chops to a warmed plate. Pour most of the fat out of the pan and add a squeeze of lemon juice to it. Stir and scrape the lovely sticky bits off the bottom and drizzle all over the chops. Remove the carrots and beets from the oven - they should be nice and sticky by now. Serve them with the chops and a glass of wine.
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