Combine 2 cups heavy cream and 1 vanilla bean in a heavy bottomed saucepot. Split the vanilla bean lengthwise and scrape the seeds into the cream, whisking gently until the seeds are fully incorporated throughout the cream. Throw in the vanilla bean pods and cook the mixture over medium heat until it begins to just simmer and the cream smells fragrant. Remove from heat and cover, allow the vanilla bean to infuse the cream for 30 minutes.
After 30 minutes, fish out the vanilla bean pods. Add 1/4 cup granulated sugar and reheat over medium heat. Don't let it come to a boil; you want it to heat just until the sugar is dissolved and the mixture is uniformly hot (but not boiling) throughout. Remove from heat and allow to cool slightly.
While the mixture is cooling, bloom the gelatin. Sprinkle 2 1/2 teaspoons powdered gelatin over the surface of 3 tablespoons water in a small bowl. Let stand for around 5 minutes, until the granules have softened completely, before scraping out into the cream mixture and whisking until the gelatin is completely dissolved. Let cool slightly for another 10 minutes, before pouring carefully into the brown butter tart crust. Transfer to the refrigerator and allow to set for at least 2 hours, until the panna cotta is firm.