Root Vegetable and Bok Choy Gratin

Name: Root Vegetable and Bok Choy Gratin
Ingredients: 3 heads of baby bok choy--cleaned, leaves separated and tough stems discarded; ½ cup dry sake; 2 garlic cloves, finely chopped; ½ medium shallot, finely chopped; 1 tablespoon finely chopped fresh thyme leaves; ½ cup whole milk; 1½ cups heavy cream; Salt and freshly ground black pepper; 2 medium celery root, peeled and thinly sliced into ¼-inch thick slices; 2 medium rutabaga, peeled and thinly sliced into ¼-inch thick slices; 4 medium yukon gold potatoes, peeled and thinly sliced into ¼-inch thick slices; 1 pound gruyère cheese, finely grated