Melt butter in a heavy saucepan over low heat; add flour, whisking until smooth. Cook, whisking constantly, 1 minute. Gradually add half-and-half; cook over medium heat, whisking constantly, until thickened and bubbly.
Whisk egg yolks until thick and pale. Gradually stir about one-fourth hot mixture into yolks; stir into remaining hot mixture. Stir in squash, salt, and nutmeg.
Beat egg whites at high speed with an electric mixer until stiff peaks form; fold one-fourth of egg whites into squash mixture. Fold in remaining egg whites; pour into a lightly buttered 2-quart souffle dish.
Bake at 350° for 1 hour or until puffed and brown.