In a large saucepan on medium heat, combine milk, butter, vanilla paste and ½ cup of the sugar. Stir together with spatula.
While saucepan is heating. Take a large bowl and hand whisk together flour and remaining sugar.
Add the eggs, yolks, and rum to the flour mixture and whisk until combined.
Carefully remove hot saucepan with milk mixture from stovetop and slowly began to pour into bowl of floured eggs. Constantly whisking as you pour.
Once fully incorporated, strain batter through a sieve.
Cover bowl with plastic wrap and place in the fridge to chill for 10-12 hrs.
The next day, set bowl on the counter to bring batter to room temperature. You will need to whisk the batter a few times.
Preheat the oben to 450 F (230 C).
Prepare your silicone mold by paining softened butter into the creases and bottom of each well using a pastry brush.
Set the mold on a flat cookie sheet on the oven for 3-4 minutes to allow the butter to melt some. This pooling of the hot butter helps with creating the dark outer texture. Remove from oven and fill the wells with batter.
Transfer batter to a container suitable for pouring. And fill each well ¾ full with batter.
Place filled silicone mold on a flat cookie sheet on the middle rack and bake for 30 minutes.
Reduce heat to 400 F (200 C) and bake an additional 15-20 minutes until dark caramelized rim forms around the edges.
Remove pan from oven and place silicone mold on a rack. While the mold is hot, using oven mits place a serving dish or flat tray on top of the mild.
Invert mold by flipping it onto the dish, allowing the hot canelés to drop.
Eat and enjoy!