Prep the carrots: Wash the carrots, remove the hard end bits and peel using a vegetable peeler not a knife. The peeler removes just the skin without taking most of the carrot too. If your carrots are large, then slice lengthways and cut the halves down again to make small sized carrots. If you are using small carrots then you don't necessarily have to cut them up.
Heat the olive oil: Use a large enough skillet or pan depending on how many carrots you are cooking. Heat 2 tablespoons of extra virgin olive oil - medium to high heat and add the carrots.
Season: Let the carrots gain cooking momentum. In other words when you see that they are sizzling away, add the salt and pepper. Move them about slightly here and there intermittently with a spatula but nothing hectic. If your stove is on a decent medium to high heat, they cook gently all by themselves. But if that doesnt happen and they cook too quickly absorbing all the liquid, then add about ¼ cup of water to prevent them from burning.
Add the next layer of flavor: Add the soft brown sugar and honey. Give the carrots a gentle nudge again with the spatula and let them cook for 8 minutes at which point you can use the tip of a sharp knife to check the tenderness. They should be ready for the final ingredients.
Finish off: Add the butter, fresh rosemary sprigg and the vino cotto. Let them cook another minute and then remove from the stove. If you added water earlier, you might want to wait for the liquid to reduce (maybe 4 to 5 mintues depending on how much water you added). Because we did not add water to this glazed carrot recipe, we can turn the heat off and tranfer them to a serving plate. If you did not add water you need to take them off the stove so that you save the liquid you have to dress over the carrots.
Serve: Top off with finely chopped fresh herbs if you wish and a sprinkle of flaky sea salt.