In a separate heavy bottom sauté pan, heat ¾ cup vegetable oil over medium-high heat until ripples form. Whisk in the cup of flour and continue stirring carefully and constantly as the roux darkens. Adjust the heat level if the roux begins to darken too fast.
Remove from heat when it attains the color of milk chocolate. Continue stirring until roux is no longer darkening. Do not allow to burn. When cooled, pour off the oil that has separated out and risen to the surface.
Whisk cooled roux into simmering broth. Return the reserved chicken and sausages. Continue to cook for about an hour, skimming oil from the surface as needed. The consistency of the gumbo should be between a soup and a stew. You can adjust the consistency to your likening by adding some of the remaining quart of broth.