Preheat the oven to 425°F (220°C).
In a 10-inch cast-iron skillet over medium heat, melt the butter. Add onion, bell pepper, and garlic; cook, stirring often, until slightly softened and fragrant (about 2 minutes).
Add flour and cook, stirring constantly, until mixture smells nutty (about 1 minute). Stir in cumin, oregano, salt, and black pepper until well combined.
Gradually stir in broth and continue to cook over medium, stirring occasionally, until thickened and smooth (about 3 minutes).
Add chicken, beans, cream cheese, salsa verde, and chiles. Cook, stirring constantly, until cream cheese is melted (about 2 minutes). Remove from heat and let the mixture cool for 10 minutes.
On a sheet of parchment paper, unfurl the pie crust and roll into an 11-inch circle. Fold dough edges under to create a 10-inch circle; crimp edges if desired. Gently place the pie crust over the filling in the skillet.
Using a paring knife, cut four 1-inch-long slits into the top of the pie crust to allow steam to escape.
Bake until golden brown and bubbly (30 to 35 minutes). Let the pie cool for 5 minutes before serving.
Enjoy your Golden Chicken Chili Pie!
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