How to Make It
Light a grill. Brush the cabbage wedges with vegetable oil and season with salt and pepper. Grill the cabbage over high heat until charred, about 3 minutes per side. Transfer to a work surface. When the cabbage is cool enough to handle, finely slice it crosswise with a sharp knife.
In a large bowl, whisk the mayonnaise with the cider vinegar, jalapeños and pickling liquid. Add the shredded cabbage and toss well. Season the grilled coleslaw with salt and pepper and toss again.
Grill the hot dog buns over high heat until crisp, about 30 seconds. Grill the hot dogs over high heat, turning several times, until lightly charred and heated through, about 4 minutes. Place the hot dogs in the toasted buns, top with the grilled coleslaw and serve.