Whisk the chicken sauce: combine hoisin, tamari, rice vinegar, Sriracha and sesame oil in a small bowl until smooth. Set aside.
Heat a large skillet over medium heat and add the neutral oil. When shimmering, add the diced onion and cook, stirring occasionally, until softened and translucent, about 4–5 minutes.
Add the minced garlic and grated ginger to the skillet and cook just until fragrant, about 30 seconds. Crumble in the ground chicken and break it up with a spatula as it browns. Cook until no pink remains, roughly 5–6 minutes.
Stir the reserved chicken sauce into the pan, scraping any browned bits from the bottom. Reduce heat to medium-low and simmer the mixture, stirring occasionally, until the sauce thickens and coats the meat, 2–3 minutes. Remove from heat and fold in the diced water chestnuts and sliced green onions; let sit 2 minutes so flavors meld.
While the chicken cooks, make the peanut drizzle: whisk together the peanut butter, tamari, maple syrup, garlic, Sriracha and lime zest. Add warm water 1 tablespoon at a time to reach a pourable drizzle consistency (about 2 tablespoons total). Taste and adjust seasoning.
Warm a second skillet over medium heat and add the cauliflower rice. Season lightly with salt and pepper, cover, and let steam for 3–4 minutes, stirring once, until tender but not mushy. Remove lid and cook 1 minute more to evaporate excess moisture.
Assemble four bowls: divide chopped romaine among bowls, then spoon cauliflower rice into one section, shredded carrots into another, and the sauced chicken into a third. Drizzle each bowl with the peanut sauce and add extra Sriracha if you like more heat. Serve immediately.