Step 1
Line a 9x9" baking pan with parchment paper, leaving overhang on 2 sides. Pulse 6 oz. gingersnap cookies in a food processor until fine crumbs form (about 2 cups). Pulse in 1 Tbsp. granulated sugar and ¼ tsp. kosher salt. Add 5 Tbsp. unsalted butter, melted; pulse until the consistency of wet sand. Transfer to prepared pan and press firmly and evenly across entire bottom with the bottom of a measuring cup. Freeze crust while you make the filling. Filling Step 2
Using an electric mixer on medium-high, beat ¾ cup heavy cream in a small bowl until stiff peaks form. Place two 8-oz. packages cream cheese, room temperature, ½ cup sour cream, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt in a large bowl; sift in 1 cup (110 g) powdered sugar. Using mixer on medium-high, beat until smooth. Mix in one 2" piece ginger, peeled, finely grated and 2 Tbsp. fresh lime juice. Scrape in whipped cream and gently fold in. Spoon filling over crust; smooth into an even layer. Freeze until filling is set, about 2 hours. Curd and assembly Step 3
Meanwhile, whisk 1 large egg, 1 large egg yolk, ½ cup (100 g) granulated sugar, ¼ cup fresh lime juice, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt in a small saucepan. Place over medium heat and cook, whisking constantly, until sugar is dissolved, about 1 minute. Continue to cook, adding 6 Tbsp. unsalted butter, cut into pieces, a piece at a time and whisking to incorporate before adding more, until all of the butter has been added and curd is thick enough to coat a spoon, 2–3 minutes. If curd is not thick by the time all of the butter has been added, continue to cook, whisking constantly, about 2 minutes more. Strain through a fine-mesh sieve into a medium heatproof bowl. Let cool slightly, then cover, pressing plastic wrap directly onto surface. Chill until cool, about 1 hour. Step 4
Scrape curd over filling; smooth into an even layer. Freeze until gently set (it will never freeze completely), about 2 hours. Step 5
To serve, run a knife along unlined sides of pan. Using parchment, pull cheesecake from pan and transfer to a cutting board. Cut into 12 bars. Top with chopped candied ginger and finely grated lime zest.
Do ahead: Bars can be made 3 days ahead. Cover and keep frozen.