In a small pot over low heat, add 1/4 cup cream, milk, sugar, 3 tablespoons butter, vanilla, and salt and bring to a simmer. Put the chocolate into a medium bowl and pour in the cream mixture. Let sit until the chocolate is melted, about 5 minutes. Add the eggs and mix until well combined.
Grease the baking dish with the remaining tablespoon of butter, and it line with the bread slices, overlapping slightly. Pour the chocolate mixture over the bread, making sure to cover the tips. Push the bread down with your fingers to coat the bread completely. Refrigerate, covered, for at least 2 hours. Remove from the refrigerator 30 minutes before baking.
Preheat the oven to 375 degrees F.
Bake until the custard sets and the bread turns golden at the edges, about 30 minutes.
Add the remaining cream to a chilled bowl and whisk until soft peaks form. Serve the French toast on individual plates with a dollop of cream.