Melt butter in a medium saucepan; add flour while stirring constantly.
Continuing to stir constantly, gradually add the milk and keep stirring until mixture begins to bubble and thicken.
Add the water, basil leaves, and salt and stir to mix well.
Taste and adjust seasonings; you might need a bit more salt and you can add some pepper if you desire.
To make stew:
In a large pot, heat the oil; add the chicken pieces and brown lightly on all sides.
Add the homemade Alfredo sauce, or, if you are using the store-bought sauce, add that to the pot along with water, basil, and salt.
Stir to mix.
Next, add the potatoes and carrots and bring to a slow simmer; cover the pot and cook the stew until the potatoes and carrots are tender and the chicken is cooked thoroughly, about 20-25 minutes.
Add the corn and peas and cook for about 5-10 minutes longer or until done.