Preheat oven to 325 degrees F. Put muffin liners in a muffin tin. Lightly spray with nonstick cooking spray.
To make the crust, in a medium bowl, combine graham cracker crumbs and melted butter until the graham cracker crumbs are evenly coated. Press a scant Tablespoon of the crust mixture into the bottom of prepared muffin cups and freeze until ready to fill.
To make the filling, in the bowl of a standing mixer, beat cream cheese and sugar on medium-high until light and smooth, about 3 minutes. Add eggs, one at a time, beating well after each addition. Add lime juice and vanilla and mix until combined. Fill each prepared muffin cup about three-quarters full.
Bake for until the cheesecakes puff up but the centers have a slight jiggle, 18-20 minutes. Cool on a rack for 10 minutes (do not turn the oven off).
Meanwhile make the topping. In a small bowl, whisk together sour cream, sugar, lime juice, and vanilla. Pour a small layer of topping over the center of each cooled cake and spread it out to the edges. Bake for 5 minutes more. Cool on a rack for 2 hours. Cover and refrigerate for at least 6 hours before serving. Top with lime slices (optional).
Cream cheese does the heaviest lifting in this dessert, demanding complete room-temperature softening before the paddle attachment touches it. Cold blocks trap air pockets and refuse to emulsify smoothly with sugar, resulting in a grainy batter that no amount of subsequent mixing will fix. Beating the base for a full three minutes incorporates the required volume while keeping the dairy pliable. Adding whole eggs sequentially rather than simultaneously prevents the emulsion from breaking, which ensures the structure stays intact during baking. The oven must remain calibrated precisely to 325 degrees Fahrenheit so the custard sets without browning the edges prematurely. Overbaking ruins the texture completely, turning a silky, velvety mouthfeel into a dry, rubbery sponge. Watch for the visual cue of a slight jiggle in the exact center of each small cake before removing them from the heat. Chilling the finished pastries for at least six hours allows the starches and fats to fully firm up, transforming a loose dairy mixture into a dense, sliceable treat. Store these desserts in an airtight container in the refrigerator for up to four days.