Preheat to 400°F or 205°C.
Sauté the vegetables: In a large oven-safe skillet or Dutch oven, melt 2 tbsp of the butter. Add the onion, celery, and carrots, and cook until softened, darkened, and lighting caramelized, about 8-10 minutes.
Bloom the aromatics: Push the vegetables to one side of the pan. Add the remaining 1.5 tbsp butter to the cleared space, then add the garlic, sage, and thyme. Cook for about a minute, until fragrant.
Make the roux: Sprinkle in the flour. Stir to coat and cook for a minute to get rid of the raw flour taste; this creates a roux.
Add stock and cream: Slowly pour in the chicken stock and heavy cream, stirring as you go. Let the sauce come together and start to thicken. Stir in the turmeric, salt, and pepper.
Add chicken and peas: Add the chicken and peas to the pan. Simmer until the chicken is warmed through and the sauce has thickened to a good gravy-like consistency but still loose, it will thicken more in the oven. Stir in a squeeze of lemon juice.