Place the chicken in a slow cooker, cover, and set to low.
Heat a saute pan over medium high heat. Melt the butter and add the flour. Stir for about 30 seconds.
Whisk in the evaporated milk, water and chicken base. Continue to whisk until the sauce thickens.
Pour the sauce over the chicken, and continue to cook for about 3-4 hours, until the chicken is cooked through.
Shred the chicken with 2 forks. Add the mushrooms, pasta, and asparagus, and continue to cook for about 30 more minutes or until the pasta is cooked through. Stir the pasta a few times while cooking. If there is not enough liquid, add up to 1/2 cup additional water for the pasta.
Sprinkle the cheese over, and stir to combine and melt. Add salt to taste and serve.