Preheat your oven to 325°F (160°C). In a medium bowl, combine crushed graham crackers, melted butter, and 1/4 cup of sugar until well blended. Press this mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes until slightly golden, then let cool completely.

In a large mixing bowl, beat the softened cream cheese until smooth using an electric mixer. Gradually add in 1 cup of granulated sugar and the vanilla extract, mixing well after each addition. Incorporate the eggs, one at a time, ensuring each is mixed thoroughly.

Gently fold in the fresh raspberries and all-purpose flour into the mixture, being cautious not to overmix.

Pour the cheesecake filling over the cooled crust and bake for 50-60 minutes until the edges are set and the center is slightly jiggly.

Once baked, turn off the oven and leave the cheesecake inside for about 1 hour to cool gradually. Then, let it cool to room temperature and refrigerate for at least 4 hours or overnight.

Before serving, garnish with extra fresh raspberries and serve with whipped cream if desired.