Heat 1 tablespoon EVOO, a turn of the pan, in a skillet over medium-low to medium heat. Add butter and melt. Add onions, garlic, thyme and bay, then stir frequently and caramelize, 25-30 minutes. Deglaze pan with wine, stir until evaporated then add stock. Bring to a bubble then reduce heat to low.
When onions are very soft but still cooking, bring a pot of water to a boil. Salt water and add pasta. Undercook noodles by a minute or so and drain.
Combine noodles with the onions and place in a casserole dish. Top with a layer of both cheeses. Cool completely for make-ahead meal before covering and storing. Or, place an oven rack in the middle of the oven and preheat broiler. Place casserole under the broiler to brown the top.