Step 1

To prepare carrots: Bring 2 inches of water to a boil in a large pot fitted with a steamer basket. Add carrots, cover and steam until barely tender, 12 to 15 minutes.

Step 2

Combine broth, vinegar, soy sauce, mustard, garlic powder and paprika in a sealable 1-gallon plastic bag. Add the carrots and refrigerate, keeping the carrots in a single layer, for at least 8 hours or up to 1 day, turning at least twice.

Step 3

Preheat grill to high or heat a grill pan over high heat.

Step 4

Remove the carrots from the marinade (discard the marinade). Grill the carrots, turning once or twice, until they're hot and have grill marks on all sides, about 5 minutes total.

Step 5

To prepare buns & serve: Grill buns until lightly toasted on all sides, about 1 minute. Brush the tops of the buns with butter and sprinkle with poppy seeds. Serve the carrots in the buns, topped with pickles, tomatoes, onion, peppers, relish, mustard and celery salt, if using.