Step 1

Whisk lime juice, maple syrup, thyme leaves, red pepper flakes, and 2 Tbsp. oil in a small bowl to combine; season dressing with salt. Set aside.

Step 2

Heat remaining ⅓ cup oil in a large heavy pot over high. Add half of cabbage, sprinkle in 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt, and cook, turning over once, until tender and charred in spots, 8–10 minutes. Transfer to a plate. Repeat with remaining cabbage and salt.

Step 3

Return cabbage to pot. Add carrots, shallot, garlic, and allspice, then pour in broth. Cover; cook until cabbage and carrots are tender, 6–8 minutes. Remove from heat. Drizzle in reserved dressing and stir to combine. Transfer to a large shallow bowl and top with scallions.