1. Preheat oven to 450 degrees. In a large saucepan, bring artichokes and milk just to a boil. Reduce heat; simmer until crisp-tender, about 10 minutes. Drain in a colander set over a bowl; reserve 3/4 cup milk.

2. In a large bowl, whisk reserved milk with creme fraiche, lemon juice, 1/4 cup cheese, thyme, salt, and pepper. Add artichokes, potatoes, shallots, and chestnuts; stir to combine.

3. Pour mixture into a 1 1/2-quart gratin dish; cover tightly with foil. Bake on a baking sheet until artichokes are tender when pierced, about 1 hour. Remove foil; sprinkle top of gratin with bread pieces and remaining 3/4 cup cheese. Continue baking, uncovered, until golden brown, 8 to 10 minutes more. Serve warm.