In a large mixing bowl, whisk together the eggs, whole milk, heavy cream, granulated sugar, vanilla extract, and salt until well combined.
Arrange the brioche slices in a greased 9x13-inch baking dish. Pour the egg mixture over the bread, ensuring each slice is well soaked. Cover the dish with plastic wrap and refrigerate for at least 2 hours or overnight for best results.
Preheat your oven to 350°F (175°C). Remove the baking dish from the refrigerator and let it sit at room temperature for about 15 minutes.
Bake the French toast uncovered for 30-35 minutes, or until the top is golden brown and the custard is set.
While the French toast is baking, prepare the salted caramel. In a saucepan over medium heat, combine the brown sugar and butter. Stir until melted and bubbly.
Carefully add the heavy cream and sea salt, whisking until smooth. Remove from heat and let cool slightly.
Once the French toast is done baking, drizzle the warm salted caramel over the top. Serve immediately, garnished with fresh berries or whipped cream if desired.