Ginger-Pumpkin Trifle with Vanilla Mascarpone Cream

Whisk together half-and-half, pumpkin, 1 cup sugar, and next 4 ingredients in a large saucepan until smooth. Place pan over medium-high heat; bring to a boil, stirring constantly. Cook, stirring constantly, 5 to 6 minutes or until mixture is thick and bubbly. Place pan in a large ice-filled bowl. Let mixture cool to room temperature, stirring occasionally. Scrape seeds from vanilla beans; combine seeds and mascarpone in a medium bowl. Beat with a mixer at high speed 2 minutes or until smooth. Gently fold in whipped topping. Whisk together coffee, hot water, rum, and remaining 1/4 cup sugar in a small bowl until sugar and coffee dissolve. To assemble trifle, spoon half of the pumpkin mixture into the bottom of a trifle dish or glass bowl; smooth top. Arrange 3 cups chopped cookies over pumpkin. Drizzle half of coffee mixture over cookies. Top with half of mascarpone mixture. Repeat with remaining pumpkin mixture, cookies, coffee mixture, and mascarpone mixture. Sprinkle evenly with 2 tablespoons cookie crumbs and candied ginger. Refrigerate at least 2 hours before serving.