In a medium saucepan or double boiler over medium heat, bring 1½ inches of water to a simmer. In a 10- to 12-cup stainless steel bowl or double boiler insert whisk the yolks and sugar until completely blended. Gradually whisk in the rum. Reduce the heat to medium-low. Place the bowl on the saucepan over, not in, the simmering water. Whisk the sabayon constantly until it thickens, foams up to double or triple in volume, and an instant-read thermometer inserted into the center registers 160º to 170ºF, 6 to 7 minutes, adjusting the heat to keep the water at a bare simmer. Be careful not to let the eggs begin to set and scrape down any splashed egg from the sides of the bowl with a silicone spatula. Remove the bowl with the sabayon from over the water and whisk gently for 30 to 40 seconds to begin cooling. Strain the sabayon through a wire mesh strainer into a medium bowl. Set aside to cool.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Prepare the grill for cooking over medium heat (400°F).
Brush the cut side of the bananas with the butter and season with 1 tablespoon of the brown sugar. In a medium bowl toss the strawberries with the remaining ½ tablespoon brown sugar; set aside. Grill the bananas, cut side down, over direct medium heat, with the lid open, until warm and nicely marked, 2 to 4 minutes (do not turn). Remove from the grill. Cool slightly, discard the peels, and chop the bananas into ½-inch rounds.
Brush the cut side of the bananas with the butter and season with 1 tablespoon of the brown sugar. In a medium bowl toss the strawberries with the remaining ½ tablespoon brown sugar; set aside. Grill the bananas, cut side down, over medium heat, with the lid open, until warm and nicely marked, 2 to 4 minutes (do not turn). Remove from the grill. Cool slightly, discard the peels, and chop the bananas into ½-inch rounds.
For each serving, add alternating layers of the sabayon mixture, banana rounds, strawberries, and almonds in a parfait glass or serving bowl. Serve immediately.
