Combine celery, sugar, and water to cover in a medium saucepan. Bring to a boil. Reduce heat; cover and simmer 20 minutes or until celery is tender. Drain well. Place celery and pecans in a lightly greased 1 1/2-quart casserole. Set aside.
Melt butter in a heavy saucepan over low heat; gradually blend in flour, and cook 1 minute, stirring constantly. Gradually add half-and-half, stirring constantly.
Gradually stir about one-fourth of hot flour mixture into egg; add to remaining mixture in saucepan, stirring well. Add salt and pepper; cook 1 minute, stirring constantly. Pour sauce over celery mixture.
Sprinkle cracker crumbs over top of casserole. Bake, uncovered, at 325° for 30 minutes.