The oven should be preheated to 425 degrees F (220 degrees C). Utilize a fork to prick the potatoes before transferring them to a baking pan measuring 10x15 inches in size.
The dish should be placed in a preheated oven and turned once to ensure even cooking. It will be ready when it reaches a tender consistency, typically after around 1 hour of baking.
In the meantime, in a large saucepan, combine ground beef, onion, and garlic. Cook the mixture over medium heat, stirring continuously to break up any clumps, until the meat is nicely browned and the onion becomes tender, which usually takes around 10 minutes. Finally, remove any excess grease.
In the saucepan, combine tomato sauce, chili beans, and chili seasoning mix. Bring the mixture to a boil and then reduce the heat to low. Cover the pan and let the flavors meld for at least 10 minutes by simmering gently.
Once the potatoes have cooled down sufficiently, take a spoon and transfer the potato pulp into a large bowl. You should have approximately 4 cups of pulp. Get rid of the skins. Next, add the broth to the bowl and proceed to mash the potatoes until they are smooth.
The butter is melted in a 4- to 5-quart Dutch oven over medium heat. Then, the flour is stirred in and cooked, while constantly whisking, to create a light roux. This process takes about 2 minutes. Gradually, the milk is whisked in, adding 1 cup at a time. While continuing to whisk constantly, the mixture is cooked until it thickens slightly. Next, the potato mixture, buttermilk, salt, and pepper are stirred in. The mixture is cooked, with frequent stirring, until heated through, which usually takes 3 to 5 minutes (note that the soup will be very thick at this stage). Finally, the Dutch oven is removed from heat and 1 cup of cheese is gradually stirred in.
The soup should be divided evenly among the bowls. Afterward, you can garnish each serving with chili, sour cream, the remaining half cup of cheese, and chives if desired.