Place the pie dough on a baking sheet and brush with a little milk. Sprinkle with the thyme and 1/4 teaspoon of the Cajun seasoning. Bake until golden brown and crisp, 15 to 18 minutes. Break into quarters.
Meanwhile, melt the butter in a large skillet over medium-high heat. Add the bell pepper, onion and remaining 3/4 teaspoon Cajun seasoning. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes. Sprinkle in the flour and cook, stirring, about 2 minutes. Gradually pour in the milk while stirring to avoid lumps. Add the potatoes and 2 cups water. Bring to boil, then reduce the heat to low and simmer, stirring occasionally, until the potatoes are cooked and the liquid is thickened, about 15 minutes. Add the chicken and jalapenos and simmer until the chicken is heated through, about 3 minutes. Thin the sauce with a little water if desired. Season with salt and pepper.
Serve in shallow bowls with a portion of pie crust.