Preheat the oven to 375°F (190°C). Grease a 9x13-inch baking dish and set aside.

Season chicken pieces with salt and pepper. Heat olive oil in a large skillet over medium-high heat and sear the chicken until golden brown and just cooked through, about 5 to 7 minutes. Work in batches if needed to avoid crowding. Remove and set aside.

In the same skillet, add broccoli florets with a splash of water. Steam for about 3 minutes until tender-crisp. Drain well and set aside with the chicken.

Melt 4 tablespoons of butter in the skillet over medium heat. Whisk in the flour and cook for 1 to 2 minutes, stirring constantly, until the mixture smells slightly nutty but has not turned brown.

Slowly whisk in the chicken stock in a steady stream, followed by the heavy cream. Bring to a gentle simmer and cook for 3 to 5 minutes, stirring regularly, until the sauce is thick enough to coat the back of a spoon.

Remove the skillet from the heat. Whisk in the sour cream, Dijon mustard, curry powder, and 1 cup of the shredded cheddar until completely smooth. Taste and adjust salt as needed.

Fold the seared chicken and broccoli into the sauce until evenly coated. Pour the mixture into the prepared baking dish and spread level.

In a small bowl, toss the crushed Ritz crackers with the melted butter until evenly coated. Scatter the remaining 1/2 cup of cheddar over the casserole, then spread the buttery crackers evenly across the top.

Bake uncovered for 30 to 35 minutes until the sauce is bubbling around the edges and the cracker topping is deep golden brown.

Let the casserole rest for 10 minutes before serving.