Preheat oven to 425 degrees F (220 degrees C). Prick potatoes with a fork. Transfer to a 10x15-inch baking pan.

Bake in the preheated oven, turning once, until tender, about 1 hour.

Meanwhile, for chili, add ground beef, onion, and garlic to a large saucepan. Cook over medium heat, stirring to break up lumps, until meat is browned and onion is tender, about 10 minutes. Drain grease.

Add tomato sauce, chili beans, and chili seasoning mix to saucepan. Bring to a boil. Reduce heat to low and simmer, covered, at least 10 minutes to let flavors meld.

When potatoes are cool enough to handle, use a spoon to scoop potato pulp into large bowl. (You should have about 4 cups pulp). Discard skins. Add broth to bowl. Mash potatoes until smooth.

Melt butter in a 4- to 5-quart Dutch oven over medium heat. Stir in flour and cook, whisking constantly to make a light roux, about 2 minutes. Gradually whisk in milk, 1 cup at a time. Cook, whisking constantly, until lightly thickened. Stir in potato mixture, buttermilk, salt, and pepper. Cook, stirring frequently, until heated through, 3 to 5 minutes (soup will be very thick). Remove from heat and gradually stir in 1 cup cheese.

Divide soup among bowls. Top with chili, sour cream, remaining 1/2 cup cheese, and chives (if using).