Prepare the Brown Butter: Place the butter in a small saucepan and cook over medium heat, stirring frequently, until butter is dark brown and very fragrant. It should have a caramelized, nutty smell. Immediately remove from the heat and allow the butter to cool for 5 to 10 minutes. Once slightly cooled, whisk in the heavy cream followed by the whole milk.
Place the brown butter mixture in a large container, cover, and refrigerate and allow the mixture to infuse together overnight.
In a large bowl, whisk together the egg yolks and ¼ cup (50 g) granulated sugar vigorously with a stiff whisk until pale yellow in color.
Stir the chilled brown butter milk mixture with a spoon, scraping the bottom and sides of the container to dislodge any large chilled butter pieces. Strain the mixture through a fine-meshed sieve into a medium saucepan. Discard the solid butter pieces (or alternatively, reserve and use for another recipe). Add the remaining ¼ cup (50 g) granulated sugar and the scraped vanilla bean seeds to the strained mixture. Place over medium-high heat and bring to a full boil. Remove from the heat immmediately.
Temper the egg yolk mixture with the hot milk mixture, whisking continuously with one hand while you pour with the other. Add the salt and mix well.
Place the custard in a clean container and allow it to chill completely in the fridge. Once chilled, stir in the mashed bananas and refrigerate overnight, or minimum of 6 to 8 hours.
Churn the ice cream mixture in an ice cream maker, according to the manufacturer instructions. Serve immediately (if you prefer a softer, froyo texture) or place in an airtight container and freeze for at least 2 to 3 hours to firm up. Cover the surface of the ice cream with plastic wrap to prevent ice crystals from forming.