How to Make It
Stir together heavy cream, 1 1/2 cups milk, brown sugar, and salt in a large saucepan. Bring mixture to a simmer over medium, whisking often to dissolve sugar.
Meanwhile, whisk together egg yolks, cornstarch, rum, vanilla, and remaining 1/2 cup milk in a heatproof bowl until smooth.
Gradually ladle about half of the hot cream mixture into egg yolk mixture, whisking constantly. Once half of the hot cream mixture is whisked into the egg yolk mixture, scrape all egg yolk mixture into remaining hot cream in pan.
Cook pudding over medium-low, whisking constantly, until bubbly and thickened, 2 to 3 minutes. Pour mixture through a fine wire-mesh strainer into a medium-size heatproof bowl. Gradually add butter pieces, whisking until butter is completely incorporated before the next addition. Press plastic wrap directly on surface of pudding; chill until set, at least 6 hours or up to 3 days.
Remove chilled butterscotch pudding from refrigerator; peel off and discard plastic. Set pudding aside.
Combine heavy cream, crème fraîche, powdered sugar, and vanilla in bowl of a stand mixer fitted with the whisk attachment; beat on medium speed until soft peaks form, 1 to 2 minutes.
Spoon about 1/2 cup pudding into each of 8 glasses. Sprinkle each pudding evenly with about 3 tablespoons crushed gingersnaps. Top each with about 1/3 cup whipped crème fraîche. Garnish with remaining crushed gingersnaps (about 1/2 tablespoon each). Serve immediately, or chill, uncovered, up to 8 hours.