Beat the eggs (whole and yolks) with the sugar using an electric mixer.
Add the flour, continuing to beat.
Add the melted butter, milk, and vanilla seeds, and beat well.
The mixture should be as smooth as a crêpe batter.
Add the coffee liqueur and rum, and mix well.
Cover the bowl with plastic wrap and refrigerate for at least 24 hours.

When using the batter, beat it again to make it homogeneous.
Pour into cannellé molds (if your mold is silicone, it is not necessary to butter it before).
Preheat your oven to 455 F (235 C), bake the cannellés for 5 minutes, then lower the oven temperature to 350 F (180 C) and continue baking for 40 minutes.
Unmold your cannellés and enjoy them warm or cold.