Preheat oven to 350°.
Combine milk, cream, garlic, thyme, and bay leaf in a small saucepan over medium heat. Bring to a simmer and remove from heat. Cover and set aside to steep for 30 minutes.
Melt butter over medium-high heat in a large saute pan or wok. Cook mushrooms, in batches if necessary, until they are soft and most of their juices have been expressed and evaporated. Season with salt and pepper; set aside.
Grease a large casserole dish.
Create three complete layers of the gratin: potatoes, parsley, chives, parmesan, mushrooms, cheddar.
Strain the infused milk and pour over the potatoes, squeezing the layers with another casserole dish or a large spatula to evenly distribute the liquid. Cover and bake for 90 minutes.
Uncover and bake for an additional 15 minutes, or until top is brown.
Let stand for 30 minutes before serving.
Times Prep time includes making sauce and the saute of mushrooms. Plus the 30 minute wait time.
Please Note: Nutritional values listed may vary from final results depending on actual measurements and brands used to prepare the recipe.