Whisk the brown sugar, white sugar, and egg yolks in a large bowl until pale yellow in color.
Whisk in the cornstarch just until combined and set it aside.
Place the sea salt, half and half, cinnamon, and nutmeg into a medium saucepan and heat it over medium-low for 4-5 minutes until bubbles appear around the perimeter of the cream mixture.
Ladle a little bit of the spiced cream mixture and whisk to combine.
Gradually pour the remaining spiced cream mixture into the egg yolks until combined.
Return the banana ice cream base to the pot, place it on the stove, and cook for 5-8minutes, constantly stirring until it thickens slightly.
Remove the banana ice cream base from the stove, pour it into a fine-mesh strainer set over a bowl, and allow the banana ice cream base to cool completely.
Place the bananas into a food processor and process them into a smooth puree.
Addthe banana puree and vanilla bean paste to the banana ice cream, cover it withcling wrap pressing the wrap directly on the banana ice cream base andrefrigerate it overnight.
Churn the banana ice cream in an ice cream machine, according to the manufacturer's instructions.
Transfer the banana ice cream to a freezer-safe container and freeze it for 4-6 hours before scooping.