### Instructions
**Part 1: The Graham Cracker Crust**
1. Preheat your oven to 325°F (160°C). Line a 12-cup muffin tin with paper liners.
2. In a medium bowl, combine the graham cracker crumbs and ¼ cup granulated sugar.
3. Pour in the melted butter and mix until the crumbs are evenly moistened.
4. Divide the mixture evenly among the 12 muffin cups, pressing firmly into the bottom of each liner to form the crust.
5. Bake for 5 minutes, then remove from the oven and let cool slightly while you prepare the filling.
**Part 2: The Cheesecake Filling**
1. In a large bowl, using an electric mixer, beat the softened cream cheese and ½ cup granulated sugar on medium speed until smooth and creamy.
2. Beat in the vanilla extract.
3. Add the eggs one at a time, beating on low speed until just combined after each addition. Be careful not to overmix.
4. Gently fold in the mashed raspberries.
5. Spoon the cheesecake filling evenly over the baked graham cracker crusts in the muffin tin, filling each liner about ¾ full.
**Part 3: Baking the Cupcakes**
1. Place the muffin tin in the preheated oven.
2. Bake for 20-25 minutes, or until the edges are set and the centers are still slightly jiggly.
3. Turn off the oven, crack the door open slightly, and leave the cheesecake cupcakes in the oven for another 15 minutes. This helps prevent cracking.
4. Remove the cupcakes from the oven and let them cool completely in the muffin tin on a wire rack.
5. Once cooled, transfer the cupcakes to the refrigerator and chill for at least 4 hours, or preferably overnight, before serving.
**Part 4: Raspberry Topping (Optional)**
1. In a small saucepan, combine the ½ cup fresh raspberries, 1 tablespoon granulated sugar, and 1 teaspoon lemon juice.
2. Cook over medium heat, stirring occasionally, until the raspberries break down and the mixture thickens slightly, about 5-7 minutes.
3. Remove from heat and let cool completely.
4. Just before serving, spoon a small amount of the raspberry topping over each chilled cupcake.
### Short Tips
* **Room Temperature Cream Cheese is Key:** Ensure your cream cheese is completely softened to avoid lumps in your cheesecake filling.
* **Don’t Overmix:** Overmixing the cheesecake batter once the eggs are added can incorporate too much air, leading to cracks.
* **Cooling is Crucial:** Chilling the cupcakes thoroughly allows them to set properly and enhances their flavor and texture.
* **Get Creative with Toppings:** While the raspberry topping is fantastic, feel free to experiment with fresh berries, a dollop of whipped cream, or a dusting of powdered sugar.
* **Storage:** Store leftover cheesecake cupcakes in an airtight container in the refrigerator for up to 3-4 days.
