In a blender, add the banana and milk, and blend until smooth. Pour the banana milk through a fine mesh sieve into a small saucepan, weighing it out to 227g (1 cup).
Place the saucepan over low-medium heat and bring the milk to a simmer, or about 190 degrees F.
Meanwhile, in a medium bowl, vigorously whisk together the egg yolks, granulated sugar, and cornstarch until pale in color and the mixture flows off of the whisk.
Once the milk has reached a simmer, slowly pour half of it into the egg-sugar mixture while simultaneously whisking to temper the eggs. Pour everything back into the saucepan and place over medium heat. Use a rubber spatula to mix constantly as it thickens.
Once the pastry cream is thick and a few big bubbles come to the surface, continue whisking for one more minute, then remove the pan from heat.
Immediately pour the pastry cream through a fine mesh sieve into a small bowl to ensure it’s perfectly smooth. Then, mix in the butter and vanilla with a rubber spatula.
Press plastic wrap up against the surface of the pastry cream to prevent a skin from forming, and place in the fridge to chill for at least one hour or until ready to use.