Preheat the oven to 250°F.
Separate the Hawaiian rolls horizontally, then divide each sliced section vertically into three evenly sized pieces.
Arrange the roll pieces in a single layer on a baking sheet. Toast for 3–5 minutes, just until they develop a pale golden color. This brief drying period helps the bread absorb the custard without becoming overly fragile.
Crack the eggs into a wide, deep bowl. Add the milk, pumpkin purée, vanilla, cinnamon, pumpkin pie spice, and salt. Whisk thoroughly until the mixture is smooth and the seasonings are evenly dispersed.
Working with a few pieces at a time, lower the toasted rolls into the pumpkin custard. Let them absorb the mixture until well coated and saturated but still structurally intact.
Lift each piece from the bowl and gently shake away the surplus custard.
Warm a large skillet or griddle over medium heat. Coat the cooking surface lightly with butter.
Arrange the soaked roll pieces on the heated surface without overcrowding them. Cook for 2–3 minutes, or until the undersides are evenly browned.
Turn each piece and continue cooking for another 2–3 minutes, until the second side is golden and the edges are lightly crisp. Apply additional butter between batches when necessary.
Transfer the finished French toast to a plate and keep it warm while the remaining pieces cook.
Serve immediately with a dusting of powdered sugar and a drizzle of warm maple syrup.