Preheat oven to 350°F. Place carrots on a rimmed baking sheet lined with foil; toss with oil. Bake carrots at 350°F for 40 to 45 minutes, depending on thickness, until fork-tender. Let cool completely. Place 3 Tbsp. water, tamari, vinegar, salt, pepper, and liquid smoke in a bowl; stir with a whisk. Set aside.  Remove skins for carrots. Use a vegetable peeler to slice carrot lengthwise into thin slices. Place in bowl with tamari mixture; gently toss to coat. Cover and refrigerate for 1 to 2 hours, or overnight. Drain excess marinade and use carrot lox as you would traditional salmon lox.