Preheat your oven to 325°F (163°C). Line an 8x8-inch baking pan with parchment paper, letting it hang over the sides for easy removal later.
In a medium bowl, combine graham cracker crumbs, melted butter, and ¼ cup of granulated sugar. Mix until well combined and crumbly. Press the mixture firmly into the bottom of the prepared baking pan to create an even crust.
Bake the crust in the preheated oven for 10 minutes. Remove and let cool slightly while preparing the cheesecake layer.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Gradually add the remaining sugar and beat until well combined.
Add the eggs one at a time, mixing well after each addition. Incorporate the vanilla extract and sour cream, then mix until fully combined and smooth.
Gently fold in the rainbow sprinkles, being careful not to over-mix as the colors can bleed.
Pour the cheesecake mixture over the cooled crust, smoothing the top with a spatula.
Bake in the preheated oven for 30-35 minutes, or until the center is set but still slightly jiggly (it will firm up as it cools).
Turn off the oven and leave the cheesecake bars inside for 1 hour to slowly cool down. Then, remove from the oven and let cool to room temperature before transferring to the refrigerator. Chill for at least 4 hours, or overnight for best results.
Once chilled, lift the bars out of the pan using the parchment paper. Cut into squares and garnish with additional rainbow sprinkles on top before serving.