Pre-heat oven to 325 degrees F. Melt 1 TBSP of unsalted butter, Brush the slices of challah bread with the melted butter. Place on a rimmed baking sheet and toast for 5-7 minutes until lightly golden brown.
Remove the challah toast from the oven. Cool and then tear into 2u0022 pieces. Set aside.
Increase oven heat to 400 degrees. Place pineapple spears on the rimmed baking sheet and sprinkle with 1 TBSP of sugar. Roast for 20 minutes until golden brown and charred on the underside, Turn the pineapple to roast on the other side. for another 15 minutes. Remove the pineapple from the oven and cut into bites sizes pieces. Toss the pineapple and the juices from the pan with the challah toast. Place the toast and pineapple in a buttered 9 x 13 baking dish.
In a large bowl, beat the eggs with the 1 cup of sugar. Add in the vanilla, ginger, salt, rum, pineapple juice, milk and heavy cream. Pour the custard mixture over challah and pineapple mixture. Top with remaining 4 TBSP of melted butter. Cover with plastic wrap tightly and chill the bread pudding for 1-2 hours or up to 8 hours-overnight.