Preheat oven to 375°F.
Lay carrots flat on a large sheet of aluminum foil or parchment. Brush with olive oil and season generously with salt. Enclose carrots in foil and fold over edges to create a sealed pouch. This will steam the carrots as they roast.
Roast carrots in pouch for 1 hour, or until carrots are very tender. There should be some caramelization on the bottoms and they should be tender enough to easily pierce with a fork. (1 hour works for me for large carrots. If you can only find small or medium carrots you might only need around 45 minutes.)
Let the carrots sit out on the. counter till they're cool enough to handle. Cut them into thin strips. (I like to cut them on a bias to get long pieces.)
Combine marinade ingredients in a sealable container. Add in the sliced carrots and toss to evenly coat them.
Seal and refrigerate for at least 4 hours, but preferably overnight. Once or twice, I recommend giving the carrots a toss with a fork, or shaking the container, to help make sure they're all marinating evenly.