To make the white sauce - in a small sauce pan, melt the 2 Tbsp butter on medium heat. Whisk in the 1 1/2 Tbsp flour, and cook for 1-2 minute.
Slowly whisk in the chicken broth a little at a time. Once all of the the chicken broth is added, bring it to a boil.
Add in sour cream, cream cheese, green chillies, Monterey jack cheese, and cumin. Whisk until well combined. Add salt and pepper to taste.
Now make the chimichanga filling by mixing the white sauce with the chicken. Place 1/2 cup of the chicken mixture on center of each tortilla. Fold the sides, then the bottom side up, to cover the filling, roll over to create chimichangas. Place on a baking sheet.
Brush each chimichangas with the melted butter and bake at 400 degrees for 15-20 minutes or until golden color.
To serve, top with shredded lettuce and salsa. Serves 6.