Heat a 4-quart stock pot or other heavy-bottomed pot over medium-high heat. Add the olive oil and butter to the pan and, once hot, add the onions, bell peppers, celery, and tasso. Cook, stirring often, until vegetables are very soft, 4 to 6 minutes. Add the garlic and cook, stirring, until the garlic is fragrant, about 1 minute. Sprinkle the flour over the vegetables and cook for 1 to 2 minutes. Add the tomato paste and the stock and season with the bay leaf, Essence, salt, crab boil and cayenne. Bring the pot to a boil and then reduce the heat to a simmer. Allow the soup to simmer for 5 minutes, then add the mirlitons and cook until just tender, about 20 minutes. Add the tomatoes and oregano and cook for 5 minutes. Add the crawfish, basil, parsley and heavy cream, stir to combine, and allow to simmer until the crawfish are heated through and the flavors have blended, about 5 minutes. Taste and re-season if necessary. Serve immediately.