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Preheat oven to 400 degrees.
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Warm olive oil in a saute pan, over medium heat. Cut chicken breasts into small pieces, season with cumin, salt and pepper, and saute in olive oil until cooked through.
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Warm tortillas in the microwave for 30 - 60 seconds, until pliable. Add 1/8 cup of cooked chicken to the center of the tortillas, and top with 2 tablespoons of shredded cheese. Roll tortillas and place seam-side down in a greased casserole dish.
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In a small saucepan, melt butter over medium heat. Sprinkle in flour, and whisk to form a roux. Slowly add in chicken broth, whisking constantly until incorporated and no clumps remain. Remove from heat.
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Add in sour cream and diced chilies and stir to combine. Add salt and pepper to taste. Pour sauce over rolled tortillas. Top with remaining cup of shredded cheese.
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Bake in preheated oven for 20 minutes.