Step 1: Preheat your oven to 325°F (160°C). In a medium bowl, combine graham cracker crumbs, 1/4 cup sugar, and melted butter. Press the mixture into the bottom of a 9-inch springform pan and bake for 10 minutes.
Step 2: In a large mixing bowl, beat the softened cream cheese and 1 cup of sugar until smooth and creamy. Add the sour cream and vanilla extract, mixing until combined.
Step 3: Add the eggs one at a time, beating on low speed just until incorporated. Do not over-mix.
Step 4: In a small bowl, toss the blueberries with 1 tablespoon of flour. Gently fold half of the blueberries into the cheesecake batter.
Step 5: Pour the batter over the pre-baked crust and top with the remaining blueberries.
Step 6: Prepare the crumble by mixing 1/2 cup flour, oats, brown sugar, and cold butter until crumbly. Sprinkle evenly over the cheesecake.
Step 7: Bake for 55-65 minutes until the edges are set. Allow to cool gradually in the oven with the door propped open for 1 hour before refrigerating for at least 4 hours.