Cook pasta according to package directions. Drain and set aside for a few minutes.
To prepare roux, melt butter into a medium saucepan over medium heat. Once melted whisk in flour, salt and pepper. Stir and cook for 3-4 minutes until color of roux will gets slightly darker. Slowly whisk in milk, stirring continuously until thickened, about 2 minutes. Reduce heat to a simmer and stir in cheese until melted.
Transfer cooked pasta to large dutch oven or pot over low heat. Pour cheese sauce over top, stirring to combine.
Add green chilies, chicken, bacon and salsa verde, stirring to combine. This is a thick and creamy sauce. To thin sauce, add additional tablespoons of milk at a time until at desired consistency.