Saute onion, carrot, celery in melted butter for 3-5 minutes until softened. Add garlic and saute for 2 additional minutes. Remove from heat and set aside.
Add chicken broth and water to a large stock pot and heat on medium-high until hot. Turn down to medium and add chicken and farro. Next, add sauteed vegetable mixture, salt, pepper and crushed rosemary and stir well. When soup starts boiling, turn down to Medium-Low or Low.
In a separate saute pan, on medium heat, melt butter and slowly add flour, whisking constantly. Turn heat down to low and slowly add skim milk, continuing to whisk until thoroughly mixed and smooth, making a roux. When thoroughly mixed and smooth, pour roux into the stockpot with the soup.
Cook for 20 to 30 minutes (uncovered) on Medium-Low heat until hot and thickened.