Put a large sauce pan on the stop top. Add in whole milk, heavy cream and vanilla extract. Heat over medium until small bubbles start to form (not a full boil). Remove from heat.
Meanwhile in a medium bowl (or stand mixer), whisk egg yolks quickly until the start to lighten a bit (this may take a few minutes).
Add sugar into egg yolks, while continuing to mix.
Carefully add about 1/4 cup of hot milk mixture into the egg mixture while stirring the whole time. (Be careful, you don't want to scramble your eggs!)
Once that is fully mixed in, add more milk 1/4 cup at a time until fully mixed, until half of the milk mixture is added.
Add the mashed banana and try to mix in as well as you can.
Pour the tempered egg mixture back into the sauce pan with the rest of the hot milk.
Cook the mixture on medium low heat until it starts to thicken, and reaches 170 degrees.
Pour the mixture into a large bowl and allow to sit at room temperature until it stops steaming.
Place bowl in the fridge and allow to cool for 1 hour, (up to overnight).
Meanwhile take peanut butter and spread it on waxed paper, like you would butter toast. Place in freezer and allow to harden.
Pour mixture into your ice cream maker and allow to mix according to directions. (We let ours mix about 45 mins)
Pull strips of frozen peanut butter off and put into your mixer and allow to mix for about 2 more minutes (or remove the ice cream from mixer and fold pb in)
Remove from mixer and enjoy now or place in a bowl with a lid to allow ice cream to harden more.