Heat butter in a medium saucepan over medium-low heat; add ham, onion, and garlic. Sauté, stirring, until onion is tender. Add chicken broth, chopped green and red tomatoes, and minced jalapeno pepper. Bring to a boil; reduce heat and simmer for about 30 minutes.
Working in batches, pulse in a blender or food processor until almost smooth. Pour back into the saucepan and add celery salt. Bring to a boil, reduce heat, and simmer, uncovered, for 5 minutes. Taste and add salt and pepper and Tabasco sauce, as desired.