Beat cream with an electric mixer on high speed until stiff peaks form. Cover and chill until ready to use.
Pour water to a depth of 1 inch into a medium saucepan; bring to a simmer. Adjust heat to maintain a simmer. Whisk together egg yolks, sugar, rum, vanilla, and cinnamon in a medium-size stainless steel bowl. Place bowl over saucepan of simmering water; cook, whisking constantly, until egg mixture thickens, about 10 minutes, stopping to scrape sides of bowl as necessary. Remove from heat; whisk until mixture is cool, 5 minutes.
Remove whipped cream from refrigerator. Gently fold egg mixture into whipped cream. Chill 30 minutes.
Place 8 graham crackers, breaking to fit as necessary, in a single layer in a 9-inch square pan. Spread 1 1/3 cups of the egg-whipped cream mixture over graham crackers. Repeat layers twice. Cover and chill 8 to 24 hours.
Just before serving, top cake with Spiced Mangoes and Sweetened Whipped Cream.