Preheat your oven to 325°F (163°C). Grease an 8x8-inch baking pan and line it with parchment paper, allowing some overhang for easy removal later.
In a medium bowl, combine the graham cracker crumbs, melted butter, and ¼ cup granulated sugar. Mix until fully combined and crumbly.
Press the crumb mixture evenly into the bottom of the prepared baking pan to form a crust. Bake in the preheated oven for 10 minutes, then remove and let it cool slightly.
In a large mixing bowl, beat the softened cream cheese with ½ cup granulated sugar until smooth and creamy.
Add the eggs one at a time, mixing well after each addition. Then, incorporate the fresh lemon juice and lemon zest, blending until fully combined.
Gently fold in the fresh raspberries, being careful not to mash them too much. This will create beautiful swirls in your cheesecake.
Pour the cheesecake mixture over the pre-baked crust, smoothing the top with a spatula.
Bake in the oven for approximately 30-35 minutes, or until the center is set but still slightly jiggly. Remove from the oven and allow to cool at room temperature.
Once cooled, place the bars in the refrigerator for at least 2 hours to chill and firm up.
Before serving, dust the top with powdered sugar and garnish with fresh mint leaves if desired. Using the parchment paper overhang, lift the cheesecake out of the pan, cut into squares, and enjoy!