Prepare the raspberry jam first so it will have time to cool a bit before adding it to the cake.
Pour the raspberries into a medium saucepan.
Sprinkle the 1/3 cup granulated sugar, 2 tbsp of cornstarch, and 1 tbsp fresh lemon juice over the berries and stir.
Cook over medium heat until the berries break down and the mixture thickens, about 10 minutes.
Place a fine mesh strainer over a medium bowl. Add the berry mixture to the strainer a bit at a time and push it through to remove the seeds. Continue until all of the jam is strained. You may need to clean the seeds from the strainer between batches.
Set aside the jam to cool.
Preheat the oven to 350 degrees Fahrenheit.
Prepare the graham cracker crust by placing 9 full sheets of graham crackers (one packet) in a Ziploc bag. Seal the bag leaving a very small opening for the air to escape.
Crush the graham crackers into fine crumbs using a rolling pin. This can also be done with a food processor.
Cut the butter into tablespoon size pieces (doesn't have to be perfect) and place in a small microwavable bowl. Microwave until completely melted, about 30 seconds.
Place the graham cracker crumbs in a large bowl. Add the melted butter and 5 tbsp of granulated sugar. Toss with a fork until the crumbs are complete moistened.
Line the bottom of a 9-inch baking pan with parchment paper. You can leave a bit of an overhang for easy lifting later.
Pour the crumbs into the bottom of the pan. Press the crumbs down in an even layer. You can start with your hands and then smooth everything out with the bottom of a dry measuring cup. Do not press too hard or the crust will become difficult to cut.
Bake the crust for 10 minutes. Make sure to let it cool completely before using.
Prepare the no bake cheesecake batter by cutting the cream cheese into large chunks.
Place the cream cheese, 1/2 cup + 3 tbsp confectioners sugar, and 1/4 cup sour cream into the bowl of a stand mixer fitted with a paddle attachment.
Mix on low speed until all of the ingredients are thoroughly blended. Set aside.
Make whipped cream for the cheesecake batter. Ideally, you will do this in a separate bowl of the stand mixer. If you don't have a second bowl to use, you can transfer the cream cheese mixture to a large bowl.
Place 1 cup of very cold heavy whipping cream into the bowl of the stand mixer fitted with a whisk attachment.
Mix on medium high speed until stiff peaks form. Be careful not to over mix as you can easily turn the cream into butter.
Gently fold the whipped cream into the cream cheese mixture using a rubber spatula. Mix until they are completely combined.
Add half of the cooled raspberry jam to the no bake cheesecake batter, folding it in until completely combined.
Pour the raspberry cheesecake batter onto the cooled graham cracker crust and smooth with an offset spatula.
Use a tablespoon to drop the remaining raspberry jam over the surface of the no bake cheesecake. Swirl it in using the back of a knife or an offset spatula. As the cheesecake filling is a rather thick mixture, this may leave grooves that don't close over. Use the offset spatula to smooth those out as well.
Cover the no bake raspberry cheesecake with plastic wrap or aluminum foil and place in the refrigerator for at least 8 hours or, ideally, overnight.
Remove the chilled cheesecake bars from the pan, lifting with the parchment paper overhand, and cut into squares. You decide the perfect size!