One day ahead, in a medium heavy-bottomed saucepan over low heat, warm the cognac and add the dried plums. The plums will absorb all the liquid and become soft and sweet. Remove the pan from the stove, cover, and set aside.

Heat the oven to 400°F / 200°C.

In a large bowl or in the bowl of a large blender, mix the eggs and additional yolk with the milk and whisk or blend until combined. Add the sugar, melted butter, vanilla, and flour and whisk or blend until smooth. Cover the bowl and place in the refrigerator to chill for 2 hours.

Butter a 12 by 8 by 2-inch / 30 by 20 by 5 cm rectangular baking 
dish and dust with flour.

Lay the plums uniformly across the bottom, then cover with the custard batter. Bake for 45 to 50 minutes until golden on the top.

Serve warm or cold, cut into rectangular pieces.