Preheat the oven to 400°F.
Bring a large pot of water to a boil. Add halved lemon, onion, thyme, garlic, and a big pinch of salt. Dip the octopus tentacles in the water a few times to curl them. Submerge, reduce heat, and simmer for 45-60 minutes or until fork tender.
Add baby potatoes to the same pot and simmer for about 10 minutes to tenderize (you can also parboil in a separate pot if easier). Remove potatoes and add to a large bowl. Toss with a liberal amount of olive oil and season with salt.
Place potatoes on an oiled baking sheet, cut side down. Roast for 18-20 minutes, flip, and roast for another 8-10 minutes or until nicely golden and crispy.
Meanwhile, add herb dressing ingredients to a small bowl and mix. Set aside.
Remove octopus and let cool slightly before cutting. Remove the mantle "head-like body" and separate the tentacles with a sharp knife.
Heat oil over medium heat in a large pan. Sear octopus for 2-3 minutes per side or until nicely browned and starting to crisp. Serve over potatoes topped with plenty of herb dressing.