Preheat oven to 325 F or 165 C and line an 8- x 8-inch square baking pan with parchment paper. I like to use metal (unpainted) binder clips to keep my parchment paper in place.
Place 1 cup of graham cracker crumbs, ¼ cup of melted butter, 2 Tbsp of sugar, and 1 Tbsp fresh lemon zest into a small bowl. Mix together until the ingredients are fully combined and the graham cracker crumbs look wet.
Pour the graham cracker mixture into your prepared pan. Use the back of a spoon or the bottom of a measuring cup to press down firmly and create a compact, even crust.
Bake for 8 minutes then remove from the oven. Place the pan on a wire rack to cool. Be sure to keep your oven on!!
While the graham cracker crust bakes and cools, make the lemon cheesecake filling.
Place 2 cups of room temperature cream cheese in a medium sized bowl. Beat with a hand mixer or stand mixer with a whisk attachment on a medium to medium high speed. Mix until the cream cheese is smooth and creamy.
Add the ⅔ cup of sugar, 1 Tbsp lemon zest, and ¼ cup of lemon juice. Mix on a medium-low speed until combined, scraping the sides of the bowl with a rubber spatula as needed.
Add in 2 eggs, one at a time. Mix on a medium speed until the eggs are fully incorporated.
Pour the lemon cheesecake on top of the cooled graham cracker crust.
In a food processor or blender, blend ¾ cup of fresh or frozen (and thawed) raspberries.
Pour the pureed raspberries into a mesh strainer to remove the seeds. Use the back of a spoon or rubber spatula to press the mixture through the strainer. Sometimes the puree sticks to the bottom of the strainer rather than dripping into your bowl, so I suggest scraping the underside of your mesh strainer with a spatula.
Stir 2 Tbsp of sugar into the raspberry puree by hand. The mixture will be quite thin, but that's how it's supposed to be!
Add spoonfuls of the raspberry mixture on top of the lemon cheesecake batter. Drag a knife or offset spatula through the cheesecake to create raspberry swirls.
Bake the cheesecake bars for 36-40 minutes. Do a wiggle test to check if they're done (watch the center, and look for a small wiggle), rather than a toothpick!
Let the bars cool completely in the pan on a metal rack. Once they reach room temperature, refrigerate them for an additional 2 hours or overnight. Do NOT put them immediately into the fridge, or the top can crack.
Top the cooled bars with an additional sprinkle of lemon zest and cut them with a sharp, warm knife. Clean the knife after each cut to get perfect squares.
Leftover bars can be kept in the fridge for up to 5 days in an airtight container.
