Special equipment: Kamado-style grill
For the octopus: Place the octopus in a pot large enough to fit comfortably and then add the vinegar, peppercorns, garlic, bay and onions. Add enough water to cover and bring to a boil over medium-high heat. Immediately reduce to a slow simmer and skim off any foam from the surface with a ladle. Simmer until the octopus is knife-tender, 45 minutes to 1 hour. Remove from the heat and let cool to room temperature in the pot with the liquid.
For the tandoori marinade: Combine the yogurt, garlic and ginger in a bowl and let sit for 15 minutes to mellow the raw garlic.
Meanwhile, heat a dry skillet over medium heat and add the paprika, peppercorns, coriander, cumin, turmeric, allspice and cardamom and toast until aromatic, turning the pan frequently to avoid burning.
Stir the toasted spices into the yogurt mixture and let sit so the flavors can come together, 10 minutes. Separate half of the tandoori marinade and reserve.
For cooking the octopus: Remove the octopus from the liquid, add to the remaining tandoori marinade and refrigerate until ready to grill.
Preheat the grill to 500 degrees F.
Sprinkle the octopus with salt and grill on the lowest rack until crispy at the ends and the flesh is heated through. Transfer to a cutting board and cut the large tentacles into individual pieces, and then in half crosswise. The smaller tentacles can be left whole. Scatter on a plate and top with the Fennel Slaw in a row down the middle. Garnish with grapefruit, lime wedges, sea salt and the remaining tandoori marinade.
Combine the pear vinegar, red wine vinegar, honey, salt, fennel seeds and 1 cup water in a saucepot. Bring to a boil, and then remove from the heat and add the celery, fennel and onions. Let steep until the liquid cools to room temperature.
Right before serving, toss the fennel fronds with the olive oil in a clean bowl. Drain the cured vegetables and transfer to the bowl. Toss well until combined.