Place a collapsible steamer in a large saucepan with a tight-fitting lid, pour in enough water to just reach the bottom of the steamer, and bring to a boil.
Break the broccoli into florets and place them in the saucepan. Steam until just tender, about 5 to 7 minutes and drain.
Preheat to oven to 350 degrees F. Butter a shallow 2-quart casserole and set side.
In a medium-size saucepan, melt the butter over moderate heat, then add the flour and stir for 1 minute. Gradually add the broth and milk and stir until thickened. Season with salt and pepper; add the nutmeg, 1/4 cup of the cheese, and the sherry. Stir until the cheese melts, and remove from the heat.
Arrange the broccoli in the prepared casserole in a single layer, sprinkle the remaining 1/4 cup cheese over the top, arrange the chicken slices evenly over the broccoli, and sprinkle the almonds over the top.
In a medium-size mixing bowl, beat the heavy cream with an electric mixer until soft peaks form, fold into the cheese sauce, pour evenly over the chicken and almonds, and bake until bubbly and golden brown, about 35 minutes.
