In a medium saucepan, combine the milk, butter, and vanilla, and bring to a simmer until the butter is melted. Remove the saucepan from the heat and set aside to cool for room temperature.
In a big bowl, combine the flour, sugar, salt. Add the eggs and yolks. Gently combine (don't whisk).
Pour the milk and butter mixture into the flour mixture. Using a spatula, gently combine. Try to avoid lumps as possible. Add the rum and combine.
Cover the bowl and refrigerate 2 or 3 days. After 1 day, stir the batter.
Preheat the oven to 230 C. Gently stir the batter. Butter the canelé molds. If you use silicone molds - skip it. Pour the batter into each mold to 1-1,5 cm from the top.
Bake for 10-15 min. Cannelés have to boil.
Reduce the heat to 190 C. Bake about 1 hour. If the cannelés puff over the molds, pull from oven and settle down. Baked cannelés should be dark brown, but not burnt.
The best texture is the same day, later the cannelés are less crunchy.