Preheat oven to 350°F. Lightly coat a 7-by-11-inch baking dish with cooking spray.
Melt 1 tablespoon butter in a large nonstick skillet over medium heat. Add cabbage and garlic; cook, stirring often, until the cabbage is just tender, 6 to 8 minutes. Transfer the cabbage mixture to the prepared baking dish. Do not wipe the skillet.
Melt the remaining 2 tablespoons butter in the same skillet. Add flour; cook, whisking constantly, until smooth and thick, about 1 minute. Stir in milk, salt and pepper; cook, whisking often, until thickened, about 3 minutes. Remove from heat; whisk in sour cream and ½ cup Cheddar until melted and smooth. Pour the sauce over the cabbage; toss to combine. Sprinkle with the remaining ¼ cup Cheddar.
Bake until the cabbage is tender and the cheese is melted, about 20 minutes. Top with bacon and chives.
