Step 1: In a large saucepan, combine the fresh blackberries, granulated sugar, and fresh lemon juice. Gently toss to coat the berries. Let sit for 10-15 minutes to allow the berries to macerate and release some juices.
Step 2: In a small bowl, whisk together the cornstarch and cold water until a smooth slurry forms with no lumps. Set aside.
Step 3: Place the saucepan with the blackberry mixture over medium heat. Bring to a gentle simmer, stirring occasionally. Cook for 5-7 minutes, or until the berries are tender but still mostly hold their shape.
Step 4: Slowly pour the cornstarch slurry into the simmering blackberry mixture, stirring constantly. Continue to cook and stir for another 2-3 minutes, until the filling thickens considerably and becomes glossy. Ensure it comes to a boil for at least one minute to activate the cornstarch.
Step 5: Remove the saucepan from the heat. Stir in the unsalted butter and vanilla extract until completely melted and combined.
Step 6: Transfer the blackberry pie filling to a heatproof bowl or container. Let it cool completely at room temperature. The filling will thicken further as it cools.
Step 7: Once cooled, use immediately in your favorite pie, tart, or other dessert. Store any unused filling in an airtight container in the refrigerator for up to 1 week, or freeze for up to 3 months.