2 1/4 teaspoons sea salt, divided, less if using salted stock
5 garlic cloves, minced
1/2 teaspoon chopped fresh sage
1/2 teaspoon chopped fresh thyme
1/2 cup dark beer, such as Guinness
2 tablespoons sweet sherry
5 cups game stock
1/4 teaspoon freshly ground black pepper
5 teaspoons freshly squeezed lemon juice
1/4 cup game stock drippings or salted butter
Eight 1/2-inch-thick slices of baguette
1/4 teaspoon sea salt
Olive oil, for the griddle
3 cups shredded Gruyère, Comte, or Swiss cheese
Thyme leaves, for garnish (optional)
Place a 5-quart Dutch oven over medium heat. Add the butter and oil and heat until the butter is melted. Reduce the heat to low and add the sliced onions and 1 teaspoon salt to the hot pan. Cook, stirring often with a wooden spoon, until the onions are deep golden brown, about 1 hour and 45 minutes.
Add the garlic, sage, and thyme to the pan and stir to combine. Continue to cook, stirring occasionally to prevent sticking, until the garlic is fragrant, about 2 minutes. Deglaze the pan with the beer and the sherry. Stir to combine, scraping the bottom of the pan to release any brown bits that may have formed. Simmer over medium-low heat until the liquid is fully reduced, about 2 minutes. Add the stock. Add the remaining 1 1/4 teaspoons salt if the stock you use is unsalted. If using salted stock, season to taste. Bring to a boil over medium-high heat. Reduce the heat to low and allow the soup to simmer for 20 to 30 minutes. Season with the black pepper and finish with the lemon juice.
When ready to serve: Preheat the oven 375℉.
Meanwhile, heat a large ovenproof skillet over medium heat. Melt the stock drippings in the pan and add the baguette slices. Flip the slices to fully coat them in the fat. Season with the salt. Place the pan in the oven and bake until golden and crispy, about 10 minutes.
When ready to serve, heat a griddle over medium-low heat.
Ladle the soup evenly among 4 bowls leaving about 1 inch of space at the top of each bowl. Brush the griddle lightly with olive oil. Sprinkle about 1/3 cup of cheese in 8 different spots on the griddle and top the cheese with a crouton. When the cheese is melted and browned in spots, use an offset spatula to scoop up the cheesy croutons and flip them one at a time on top of the soups, placing 2 croutons on each serving. Sprinkle with thyme leaves if using and serve immediately.