1. Preheat oven to 350°F.
2. Arrange baguette slices on a baking sheet; bake 10 to 12 minutes or until lightly toasted.
3. Let cool completely (see Tips).
4. Turn the oven off.
5. Butter a 9 x 13-inch baking dish. Heat 2 Tbsp. oil in a wide, heavy-bottomed saucepan or skillet over medium-high heat.
6. Add mushrooms and a pinch of salt and cook 5 to 8 minutes, stirring often, until the mushrooms have reduced in volume by half and have started to brown.
7. Transfer to the buttered baking dish. In the same pan, heat butter and remaining 1 Tbsp. oil over medium-high heat.
8. Add onions and cook about 20 minutes, stirring every few minutes and lowering the heat as needed to prevent scorching, until the onions are soft and golden brown.
9. Add wine and scrape the bottom of the pan to dislodge any brown bits, stirring until the wine has evaporated.
10. Add onions to the mushrooms and arrange in an even layer.
11. Shingle toast pieces into three rows, lengthwise, over the top.
12. In a medium bowl, whisk together stock, egg and thyme; pour evenly over the toast.
13. Let sit for at least 15 minutes or up to 30 minutes so the stock can soak into the bread, or cover and refrigerate overnight, removing the stuffing 30 minutes to 1 hour before baking.
14. Preheat oven to 350°F.
15. Sprinkle cheese evenly over the stuffing and bake 30 minutes or until the cheese has melted and the stuffing is at least 165°F in the center and bubbling on the sides.
16. Sprinkle with thyme, if desired, before serving.

TIPS:

Gruyere, a sharp tasting cheese, is the classic cheese for French onion soup. You can use a mix of Gruyere and other sharp cheeses, like Parmesan or aged Cheddar.

To work ahead, toast the bread a couple of days in advance and then keep it in a sealed bag. The drier the bread, the better it absorbs the stock.