Preheat oven to 175°C (347°F). Place an oblong casserole dish inside to preheat.
Heat fat in a large pan over medium-high heat.
Season chicken breasts with salt and pepper. Sear for 3–4 minutes per side until golden brown.
While chicken sears, mix the cheese, breadcrumbs, a splash of cream, chopped parsley, chopped chives, and finely chopped onion. Season with salt and pepper.
Pour poultry broth around the seared chicken in the pan.
Transfer fillets to the preheated casserole dish, leaving the broth in the pan.
Add the remaining cream to the broth in the pan and bring to a boil, stirring for about 1 minute.
Pour the cheese and herb mixture onto the fillets in the casserole. Stir any remaining mixture into the sauce in the pan, bring to a boil for about 1 minute, then pour the sauce next to the fillets in the casserole.
Bake uncovered at 175°C (347°F) for 15–20 minutes, until the chicken reaches 74°C (165°F) internally.
Serve with colorful vegetables, young potatoes, or rice.