For crispy chili oil, in mortar and pestle, or by hand, roughly crush dried chili peppers. Wash hands well. Transfer chilies to heatproof jar or medium bowl and add ginger, garlic, green onion, star anise, and sesame seeds.
In small skillet, heat 1/4 cup vegetable oil over low heat. Add Sichuan peppercorns and cook for 1 minute. Remove peppercorns and discard, reserving oil. Heat oil until shimmering, but not smoking. Pour over spices in jar. Stir and infuse for 1 minute before adding vinegar, soy sauce, salt, and 1 Tbsp water. Stir to combine.
Preheat grill. In large bowl, toss Brussels sprouts with 1 tsp olive oil. Add Brussels sprouts directly to grill if gap between grates is narrow or skewer sprouts (pre-soak for 30 minutes if using wooden skewers) before adding to grill. Grill for 10 minutes. Turn and grill for 15 to 20 minutes more, until charred and tender.
In blender or food processor, purée garlic, ginger, miso, dried chili pepper, soy sauce, and rice vinegar. If needed, add 1 Tbsp water to help blend.
Cook buckwheat noodles according to package directions. Drain and rinse. Leave to soak in cold water until needed so noodles don’t stick.
Heat remaining 1 tsp olive oil in large pot over medium heat. When hot, add garlic purée and cook for 2 minutes, stirring frequently. Add tofu cubes and half the green onions. Cook for 1 minute. Add sake or mirin.
Re-drain noodles and stir into pot. Remove pot from heat. Divide among 6 bowls and top with roasted Brussels sprouts. Drizzle with crispy chili oil and garnish with remaining green onions.