If starting from raw, poach the octopus (1 hour to 1 hour 15 minutes). Bring the poaching liquid to a boil, dip the octopus in and out three times so the tentacles curl, then submerge it and keep the water at a bare simmer. Weigh it down with a small heatproof plate if it bobs up. It is ready when a paring knife slides in easily at the thickest part. Turn off the heat, let it sit in the liquid for 15 minutes, then cool it on a board. Skip this step if your octopus is already cooked.
Heat the oven. Place a rack in the middle and heat the oven to 220°C (425°F). Line a large sheet pan with parchment.
Prep the kohlrabi (about 10 minutes). Cut off the stems and roots, peel off the tough outer skin with a vegetable peeler, and cut the bulbs into 1/2-inch (1.3 cm) pieces. Toss them with the oil and salt, and spread them in a single layer with space between pieces.
Roast the kohlrabi (15 minutes). The pieces should begin to turn golden at the edges and smell sweet and nutty.
Mix the glaze and dry the octopus. While the kohlrabi roasts, whisk the gochujang, honey, soy sauce, vinegar, sesame oil, garlic, and warm water until smooth. Cut large tentacles into 3-inch (7.5 cm) pieces and pat everything very dry with paper towels. Dry octopus chars. Wet octopus steams.
Add the octopus (10 minutes). Push the kohlrabi aside and add the octopus to the pan. Roast until the tentacle tips look darker and slightly crisp and the thicker parts are hot.
Glaze (about 4 minutes). Brush the octopus with about half of the glaze and roast until it turns glossy, sticky, and deep red-brown at the edges. Watch closely, because honey and gochujang darken fast.
Finish and serve. Toss the octopus and kohlrabi with the remaining glaze, sprinkle with green onions and sesame seeds, and serve with lime wedges. The kohlrabi should be tender in the center and golden at the edges.