Warm the cream in a pot. In a second pot, simmer 100 g sugar and 1 tablespoon water until a golden yellow caramel is formed. Add the cream carefully and let it simmer for about 3 minutes until the caramel has dissolved.
Remove the pot from the stove and let it cool down for about 5 minutes. Cut salted butter into pieces and stir in. Let the sauce cool down while stirring occasionally.
Mix milk, 2 tablespoons of sugar and rum in a deep plate. Whisk eggs. Leave slices of bread to stand in the milk for 1/2 minute on each side. Drain and pull through the eggs.
Melt butter in 2 portions in a pan. Bake slices of bread in it in 2 portions on each side for 2-3 minutes until golden brown. Arrange on plates and drizzle with caramel sauce.