Use a microwave oven to warm the Half & Half slightly.
Place the mushrooms in a mixing bowl, pour the cream over them and let them to sit for about 15 minutes.
Melt the butter in a saucepan over medium heat. Add the flour to the butter a little at a time, stirring constantly, to make a roux.
Slowly whisk in the cream and morels, keeping the saucepan over medium heat until the mixture begins to thicken.
Add the cheese, cayenne and mustard, continuing to cook until the cheese is completely melted and smooth.
Add salt and pepper to taste.
Serve over toasted bread or English muffins.