Preheat the oven to 400 degrees F. Grease 4 single-serving clay pots or souffle dishes.
In a pan set over medium-low heat, add the butter and oil. Add in the onions, green peppers and garlic and saute until the onions are transparent. Add the crawfish, seafood seasoning and red pepper, and cook 2 minutes stirring frequently. Add the cream cheese and stir until melted, then add the half-and-half. Add half of the asiago and stir.
Cut the puff pastry to fit the shape of the serving dishes, and then set aside.
Divide the mixture into the prepared dishes. Sprinkle with remaining asiago, then place the puff pastry on top. Brush the egg wash over the pastry, then bake until the tops are golden, 15 minutes. Serve hot.