Preheat oven to 350°F. Place sausage and onion in a large skillet over medium, and cook, stirring often, until sausage crumbles and is no longer pink and onion is translucent, 6 to 8 minutes. Transfer mixture to a plate lined with paper towels to drain. Wipe skillet clean.

Reduce heat to low, and add 1/4 cup of the butter to skillet; cook, whisking often, until melted. Whisk in flour until smooth. Cook, whisking constantly, 1 minute. Gradually whisk in milk; increase heat to medium, and cook, whisking constantly, until thickened and bubbly, 5 to 6 minutes. Whisk in shredded cheese, and cook, whisking often, until cheese is melted and mixture is smooth, 30 to 40 seconds. Stir in sausage mixture, salt, and pepper.

Transfer mixture to a lightly greased (with cooking spray) 13- x 9-inch baking dish. Arrange biscuits on top of sausage mixture. Bake in preheated oven until biscuits are golden brown and gravy is bubbly, 30 to 35 minutes. Microwave remaining 1 tablespoon butter in a small microwavable bowl on HIGH until melted, about 20 seconds. Remove casserole from oven; brush biscuits with melted butter, and sprinkle with chives. Let stand 10 minutes before serving.