Heat butter and oil over medium-low heat in a medium saucepan.
Add chopped garlic, onions, peppers, and celery. Sauté the vegetables for about 5 to 7 minutes, until just tender.
Meanwhile, combine the paprika, Creole seasoning, thyme, oregano, basil, Worcestershire sauce, hot sauce, and ground pepper in a small cup.
Stir tomatoes into the vegetables then add the seasoning mixture. Sauté for 1 minute longer.
Add chicken or vegetable stock and bring to a boil. Stir in the sliced green onions.
Add cooked chicken to pot.
Continue boiling, uncovered, for 10 minutes. Much of the liquid will cook away.
Stir in the tomato paste and butter until well blended into the sauce.
Serve immediately over mofongo in large, deep dish or bowl.