Preheat oven to 425F.
Season chicken with salt and black pepper.
In an oven-safe pan with lid (e.g. cast iron), heat olive oil at high heat, put chicken thighs skin side down until brown, about 5 minutes. If desired, also cook on other side.
Reduce to medium-high heat, add onion, cook until lightly browned (about 5 minutes)
Add garlic, half of thyme leaves, tomato paste, stir and cook for 1 minute.
Put chicken skin side up, add water for reducing, and cook 10 minutes until reduced, stirring occasionally.
Take out chicken, add water and salt for cooking, break spaghetti into thirds, add and submerge. Add chicken back with skin side up and bring to a simmer.
Cover with lid and put in oven for 30 minutes.
Meanwhile, mix parmesan, breadcrumbs, parsley, lemon zest, remaining thyme leaves.
Remove pot from oven and set to broil.
Sprinkle breadcrumb mix on top, drizzle with remaining olive oil, broil for about 4 minutes without lid.
Allow to settle for 5 minutes before serving.