Combine eggs, sugar, mustard, vinegar salt, and butter into a large saucepan. Bring to a boil, stirring constantly. Lower heat and let simmer until thickened. (Stir constantly). About 3-5 minutes. Remove from heat and let cool. Meanwhile, combine macaroni, celery, onion, ham, cheese, salt, pepper, and frozen peas into a large bowl. Add the mayo, sweet relish, and the half and half to dressing.  Pour dressing over salad and mix well. Chill until ready to serve.