Step 1

Preheat the oven to 350 ̊. Place a 9-by-13-inch baking pan of hot water on the bottom oven rack. For the crust: Line a second 9-by-13-inch baking pan with foil and coat with cooking spray. Pulse the graham crackers in a food processor until fine crumbs form. Pour in the butter and pulse until the crumbs are well coated and stick together when pinched. Press evenly into the bottom of the prepared pan.

Step 2

For the filling: Beat the cream cheese, granulated sugar, lime juice and vanilla in a large bowl with a mixer on medium speed until smooth and light, 2 to 3 minutes. Add the eggs, one at a time, beating well after each addition. Add the sour cream and beat until just incorporated, 1 minute.

Step 3

Pour the filling over the crust and smooth the surface. Bake until the center is just set but still slightly jiggly, about 45 minutes. Turn off the oven and leave the bars in the oven with the door closed for 10 minutes. Open the door halfway and leave the bars in the oven until firmly set around the edges and barely jiggly in the center, about 10 more minutes. Remove from the oven and let cool to room temperature, about 30 minutes, then refrigerate until cold, at least 1 hour and up to 24 hours.

Step 4

When ready to serve, remove the bars from the pan and peel off the foil. Cut into pieces and generously dust with powdered sugar.