Line a 24-cup mini muffin pan with paper candy liners. Melt about two-thirds of the white chocolate with the optional coconut oil or vegetable shortening in 20-to-30-second microwave intervals, stirring after each interval, or melt it gently over a double boiler.

Spoon approximately 1 teaspoon of melted white chocolate into each liner. Brush or tilt the chocolate up the sides to create an even shell, then chill for 10 to 15 minutes until firm.

Combine the pumpkin purée, brown sugar, pumpkin-pie spice, butter, and salt in a small saucepan. Cook over medium-low heat for about 5 minutes, stirring frequently, until the mixture is hot, thickened, and slightly reduced.

Remove the pumpkin mixture from the heat and stir in the vanilla and graham-cracker crumbs. Let the filling cool until warm or room temperature rather than hot.

Spoon roughly 1 teaspoon of cooled filling into each chocolate shell, leaving enough space for the top chocolate layer. Re-melt the remaining white chocolate if necessary and spread it over each cup to seal in the filling.

Chill the completed cups for 30 to 60 minutes, until completely firm. Garnish with a small amount of graham-cracker crumb or pumpkin-pie spice before serving.