Heat 2 tablespoons butter and 2 tablespoons olive oil in a large deep skillet or Dutch oven over medium heat. Add sliced onions and a pinch of salt; cook, stirring occasionally, until deep golden and jammy, 18–25 minutes.

Stir in garlic, tarragon, thyme, remaining salt, and pepper; cook 60–90 seconds until fragrant.

Deglaze with 1/3 cup chicken stock and apple cider vinegar, scraping up browned bits. Add Worcestershire sauce and simmer 1 minute.

In a small skillet, heat remaining 1 tablespoon butter and 1 tablespoon olive oil over medium-high. Sauté mushrooms in a single layer until browned, 6–8 minutes. Season with a pinch of salt and add to the onion mixture.

Stir uncooked rice into the onion-mushroom mixture until coated. Fold in spinach to wilt.

Pour in 3 cups chicken stock and the heavy cream; stir well and taste the liquid, adjusting salt if needed. Bring to a gentle simmer.

Fold in the cooked, torn chicken. Transfer mixture to a buttered 9x13-inch baking dish and smooth the top.

Sprinkle shredded Gruyère evenly over the surface. Cover with foil and bake at 375°F (190°C) for 30 minutes.

Remove foil and bake 10–15 minutes more, until bubbling and golden on top. Rest 5–10 minutes; garnish with parsley and serve warm.