In a medium saucepan or double boiler over medium heat, bring 4 centimetres of water to a simmer. In a 2.3 to 2.8 litre stainless steel bowl or double boiler insert and 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 centre reaches 70ºC to 77ºC, 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 (180°C to 230°C).
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 of 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 1 centimetre 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 of 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 1 centimetre 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.
