Prep: Peel 6 carrots and trim off the ends, cutting them to fit into the bottom of your large pot.
Boil: Stir together 2 cups vegetable broth, ½ cup apple cider vinegar, 4 Tbsp soy sauce, ¼ cup Dijon mustard, 2 tsp smoked paprika, and 1 tsp liquid smoke in a large pot. Add carrots, cover, and bring to a simmer over medium/high. Cook for 15 to 20 minutes, or until carrots are cooked through. You should be able to pierce them with a fork, but they should not be so soft that they break easily.
Marinate: Let carrots rest in the cooking liquid for 30 minutes.
Serve: At this point you can serve the carrots, or you can sear them on a well-greased grill (or grill plate) to char the outsides. Serve on a hot dog bun with your favorite condiments!
