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Cook pasta according to package instructions.
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Meanwhile, sprinkle chicken with ¼ teaspoon salt and ⅛ teaspoon pepper.
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Heat oil in a large skillet over medium-high heat. Add chicken and cook about 3 minutes. Add chili powder, ground cumin, and garlic; cook 1 minutes, stirring frequently. Add tomatoes and green chiles; bring to a bubble and cook for about 2 minutes.
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In a small bowl, whisk the flour into the milk. Gradually add this mixture to the chicken mixture and stir to combine. Cook until thickened, stirring frequently, about 3 minutes. Remove from heat and stir in cheese until melted. Fold in the pasta. Add the remaining salt and pepper. Serve hot.