Heat the olive oil in a large Dutch oven over medium-high heat and add the venison stew meat. Cook until browned on all sides, stirring occasionally. Once browned, remove from the Dutch oven and let rest at room temperature.

Place the same Dutch oven back on the stovetop. Add the butter and the sliced onions. Cook on medium heat. Let the onions cook until they are caramelized, stirring occasionally for around 30 minutes. The onions should take on a deep golden color. Once the onions are caramelized, add the sliced garlic and cook for an additional minute.

Increase the heat to medium-high. Pour in the red wine and Madeira wine. Scrape the bottom of the pot to deglaze it, releasing any of the fond stuck to the bottom. Let the wine simmer for a few minutes to reduce slightly. Add the beef or venison broth and Worcestershire sauce to the pot. Bring the soup to a boil, then reduce the heat and let it simmer for about 1 hour, or until the venison is tender.

Preheat your broiler while the soup is simmering. Arrange the baguette slices on a baking sheet and toast them under the broiler until golden brown on both sides.

When the soup is done simmering, add the chopped thyme and adjust the seasoning with salt and freshly cracked black pepper. Ladle the soup into oven-safe bowls or crocks. Place a toasted baguette slice on top of each bowl of soup. Sprinkle a generous amount of grated Gruyère cheese over each baguette slice, making sure to cover it completely.

Place the bowls of soup on a baking pan. Place under the broiler until cheese is melted and has a bubbly “crust.”

Remove the bowls from the broiler and let them cool for a few minutes before serving.