Preheat oven to 350°. Oil or spray an 8 x 8-inch dish and set aside. Toast the bread and spread with 2 tablespoons butter. Cut into 1-inch squares and set aside. Steam the broccoli florets for 3–4 minutes, rinse under cold water, and set into a colander to drain until needed.
Bring the chicken stock to the boil over medium-high heat in a medium stock pot. Add chicken, reduce heat to low, cover and simmer chicken 15–18 minutes. Remove chicken to a cutting board and let stock cool. Cut chicken into small bite-sized pieces.
Melt the remaining butter in a saucepan over medium-low heat. Whisk in the flour and stir briefly to incorporate the flour and butter, about 1 minute. Stir in 2 cups broth from cooking the chicken. Whisk constantly until smooth. Whisk in cold milk and reduce heat to simmer. Continue whisking until smooth, about 1–2 minutes. Continue cooking until thickened. Stir in sherry, mustard, salt, pepper, and nutmeg or curry powder and remove from heat.
Coat the bottom of the prepared dish with a third of the sauce. Scatter one half of the broccoli florets over the sauce. Toss half of the chopped chicken over the broccoli. Sprinkle with half of the cheese. Pour one third of the sauce over the cheese. Repeat with another layer, using all the remaining sauce over the chicken. Sprinkle with Parmesan cheese and top with toast squares. Bake the chicken dish 35–45 minutes, until bubbly. Serve hot.