In a sauce pan, mix the milk and the cream and add the vanilla (and cinnamon, if using) and the sliced pieces of the bananas. Bring to a simmering almost-boil, then take off from the heat and let cool down.
When cooled down, cover and put aside in the refrigerator to seep for, preferably, at least 24 hours.
Once the infusion is over, sieve off the banana pieces from the dairy: gently use a spatula or similar to extract as much of any remaining liquid still clinging to the banana pieces. Discard what is left of the banana pieces and prepare the final custard base.
Mix the banana flavoured dairy with the sugar(s) and the egg yolks.
While stirring frequently, bring the base up to 85 degrees Celsius/185 ยบ F: the so-called Nappe stage. Take off from the heat, let cool down and then refrigerate covered for at least 24 hours.
Churn the chilled custard base in your ice cream machine, or still-freeze using only your kitchen freezer (see separate post here on the blog on how to best do this!)