Bring a pan of water to a boil with carrot, celery, peppercorns, thymes, and lemon.
Plunge the octopus tentacles into water. Decrease heat to low and simmer for 45-60 minutes until octopus becomes tender or until a small knife pierces easily through the thickest part of the tentacle.
Remove octopus from cooking liquid and let it cool. Discard cooking liquid.
Combine 2 tablespoons of olive oil, garlic, and salt in a bowl. Add octopus and toss to coat.
Heat a heavy-based grill pan over high heat or preheat the barbeque to high.
Sear octopus for 2-3 minutes on each side until the tentacles have a few char lines and become crispy.
Remove tentacles from heat and transfer to cutting board. Use a sharp knife to slice tentacles into ¼ inch thick.
Transfer tomatoes to a serving platter. Top with octopus. Garnish with mint leaves and Aleppo pepper. Lightly drizzle with olive oil and lemon juice. Sprinkle lightly with salt and pepper to taste. Serve immediately.