Spray square 2-quart baking dish with nonstick spray.
In bowl, whisk milk, eggs, mustard, thyme, and ¼ tsp. each salt and pepper to blend.
Arrange half of bread, overlapping, in baking dish. Pour half of milk mixture over bread; sprinkle with half of cheddar. Top with ham, then repeat layering of bread, milk, and cheddar. Cover dish; chill 1 hour or up to overnight.
Heat oven to 350°F. Uncover and bake until golden and custard is set, 50 to 55 minutes. Let stand 5 minutes before serving. Garnish with chives.
