Combine all the ingredients and thoroughly mix with a hand or stand mixer on medium speed
Adjust the oven rack to the center position, with a lower oven rack in place for the water bath described in step 5, and preheat the oven to 350 degrees fahrenheit.
Make the crust first by putting graham crackers in food processor to pulse them into fine crumbs Pour crumbs into a medium bowl and stir in sugar and melted butter until combined. Mixture will be sandy still. Press firmly into the bottom and slightly up the sides of a 9 inch springform pan. No need to grease the pan. I use the bottom of a measuring cup to pack the crust down tightly. Pre-back for 8 minutes. Remove from the oven and allow the crust to slightly cool as you prepare the filling.
Using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese and sugar together on medium-high speed in a large bowl until the mixture is smooth and creamy, about 2 minutes. Add the juice, sour cream, vanilla extract, and lime zest then beat on medium-high speed until fully combined. On medium speed, add the eggs one at a time, beating after each addition until just blended. After the final egg is incorporated into the batter, stop missing. To help prevent the cheesecake from deflating and cracking as it cools, avoid over-mixing the batter as best as you can.
Boil a pot of water. You need 1 inch of water in your roasting pan for the water bath, so make sure you boil enough. Place a large metal baking or roasting pan (do not use glass) on the bottom oven rack of the preheated oven. Pour boiling water into a pan, about 1 inch deep. Immediately place the cheesecake on the center rack. Close the oven to trap the steam inside. This unique water back adds steam to the oven without having the cheesecake sit inside the water itself. Tent with aluminum foil if top starts to brown too fast.
Bake cheesecake for 55-70 minutes or until the center is almost set. When it's done, the center of the cheesecake will slightly wobble if you gently shake the pan. Turn the oven off and open the oven door slightly. Let the cheesecake sit in the oven as it cools down for 1 hour. Remove from the oven, then cool cheesecake completely at room temperature. Then refrigerate the cheesecake for at least 4 hours or overnight.
Use a knife to loosen the chilled cheesecake from the rim of the springform pan, then remove the rim. Add optional toppings if desired.
Optional Jelly Layer Topping
Mix together the sugar, cornstarch and the agar powder in a small bowl. Add a few Tablespoons of the water and stir until the dry mix has dissolved.
Pour mixture into a pan with the rest of the water, the lime juice and a drop of green coloring. Turn the heat up to medium-low and bring to a simmer, stirring continuously. Allow to simmer for 1 minute. The agar will only set once you reach boiling point so make sure it gets there. Take it off the heat and wait 10 minutes for it to cool slightly.
Gently pour the jelly onto the fully cooled and set cheesecake layer. Chill for at least one hour. Pipe on some whip cream and garnish with raspberries and super thin lime slices if you wish.