Preheat your oven to 350 degrees.
Make the crust. Mix the graham cracker crumbs and brown sugar together in a bowl. Stir in the melted butter until thoroughly blended. Press the mixture evenly into the bottom of a springform pan. Bake in the oven until golden brown, about 8 minutes. Remove from the oven and let it cool.
Make the filling. Place the cream cheese in a mixing bowl and beat until smooth and creamy, about 2 minutes. Keep beating while you gradually add the sugar. Then add the egg yolks, one at a time, scraping the sides of the bowl after each one. Add the limoncello and sour cream and mix until they are combined well.
Next beat the egg whites in a clean bowl until soft peaks form. Continue beating while gradually adding 1/4 cup sugar in a slow stream, until stiff peaks form. Be careful not overbeat. With a spatula, gently fold 1/3 of the meringue into the cream cheese mixture. Repeat twice more with remaining meringue, mixing carefully and doing your best not to deflate the egg whites. Mix until you don't see any large streaks of meringue. Pour the filling onto the crust, and place in the oven. Pour hot water into a pan and place in the oven beside or under the cheesecake.
Bake in preheated oven until the top is almost set (it doesn't jiggle when you move the pan), about 50-55 minutes. Turn off the oven, prop the oven door open about 2 inches, and allow the cake to cool completely in the oven, about 1 hour. Pop in the fridge and chill for at least 4 hours, or overnight before serving.
Make the topping. Add the raspberries and the raspberry liqueur (and the sugar depending on if you are using store bought liqueur or homemade) to a medium pot and bring to a low simmer. Simmer for about 7 or 8 mins until the raspberries have broken down a bit. Mash them up a bit with a fork. If you want you can strain the whole works or you can strain half. We like to just strain half.
When you are ready to serve the cake, slide a knife between the cake and the pan to loosen it from the edges. Open the springform pan and slide the sides off. Place on your serving platter or cake stand and pour the raspberry sauce over the cake. Top with fresh raspberries and serve!