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1
Bring the rice and water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover, and simmer until the rice is chewy and the liquid has been absorbed, about 15 minutes. Let the rice stand, covered, for about 5 minutes. Uncover, and allow to cool.
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2
Preheat oven to 400 degrees F (200 degrees C). Grease a 9-inch pie dish.
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3
Place the sausage links into a large skillet over medium-high heat, and cook until browned on both sides, 3 to 4 minutes per side. Remove from heat, and cut into 1/4 inch slices; set aside. Melt butter in a large saucepan over medium heat, and whisk in flour. Allow the flour to cook until frothy-looking, about 1 minute; whisk in the milk. Turn the heat down to medium-low, and simmer the sauce while you finish the remaining steps; whisk often. Stir in Cajun seasoning to taste. When sauce has thickened enough to coat the back of a spoon, remove from heat.
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4
In a bowl, toss the chicken meat with liquid smoke flavoring. Mix in the cooked rice, cooked sausage, onion, red bell pepper, garlic, and shrimp until thoroughly combined. Pour in about 3/4 of the white sauce to moisten the filling.
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5
To assemble the pie, trim the sheets of puff pastry to 10x10 inches; lay a sheet in the prepared pie dish. (Square corners will stick out). Fill the bottom crust with the rice mixture, and pour in the remaining 1/4 of the white sauce. Top with the remaining sheet of puff pastry; pinch the edges to seal. Brush the top of the pie with beaten egg.
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6
Bake in the preheated oven until the crust is flaky in the center and golden brown, 20 to 30 minutes.
