Add the ham, mayonnaise, mustard, horseradish, hot sauce, garlic powder, onion powder, celery seed, pepper, paprika and caraway seeds (if using) to a food processor. Pulse to puree the ingredients to desired texture.
Stir in chopped celery and chopped onion, and cover and chill in refrigerator until ready to serve.
It makes a great appetizer spread to serve with dry crackers. Or, it's also great as a sandwich spread.