Step 1: Prepare the Pickle-Brined Strawberries (Optional, but Recommended). In a small bowl, combine the dill pickle brine and water. Add the reserved 1/2 cup of finely chopped strawberries to the brine. Let them sit at room temperature while you prepare the other components, or refrigerate for up to an hour.

Step 2: Make the Crust. To a food processor, add the graham crackers and brown sugar. Process until finely ground, about 1 minute. With the processor running, slowly pour in the melted butter. Process the mixture until it is the texture of coarse sand. Stir in the dill pickle powder.

Step 3: Press Crust into Pan. Spray a 9-inch springform pan with cooking spray. Transfer the graham cracker mixture to the pan. Using a measuring cup, press the mixture into the bottom and about 1 ½ inches up the sides of the pan. Press firmly to pack and make an evenly thick crust.

Step 4: Freeze Crust. Place the crust in the freezer for 20 minutes.

Step 5: Whip the Cream. To the bowl of a stand mixer fitted with the whisk attachment, add the heavy cream and vanilla. Mix on medium-high speed until very stiff peaks form, 1 to 2 minutes. Transfer the whipped cream to a mixing bowl.

Step 6: Beat the Cream Cheese. To the same stand mixer bowl, add the cream cheese. Fit the mixer with the paddle attachment and beat the cream cheese on medium speed until softened and smooth, 1 to 2 minutes.

Step 7: Add Sugars and Lemon. Scrape down the sides of the bowl, and add the granulated sugar, powdered sugar, lemon zest, and lemon juice. Beat to combine on medium speed until smooth, 1 minute.

Step 8: Dissolve Gelatin. In a medium bowl, combine the strawberry gelatin with the boiling water. Whisk vigorously for at least 2 minutes to dissolve the gelatin, scraping any sugar from the sides of the bowl as you whisk.

Step 9: Combine Gelatin and Cream Cheese. Add the gelatin mixture to the cream cheese mixture. Beat on medium speed until very smooth, scraping the sides and bottom of the bowl as needed, about 1 minute.

Step 10: Fold in Strawberries. Drain the pickle-brined strawberries. Fold all the strawberries (brined and regular) into the cream cheese mixture.

Step 11: Fold in Whipped Cream. Add one-third of the whipped cream to the cream cheese mixture and gently fold in with a rubber spatula until completely combined. Add the remaining two-thirds of the whipped cream and continue to gently fold until completely combined.

Step 12: Assemble Cheesecake. Remove the crust from the freezer and add the filling. Gently push into an even layer and smooth the top with the back of a spoon or an offset spatula.

Step 13: Chill. Cover the pan with plastic wrap and refrigerate for at least 12 hours and up to 2 days.

Step 14: Serve. Loosen the cheesecake from the springform pan with a small knife or offset spatula. Transfer the cheesecake to a serving platter or cutting board. Cut slices with a warm knife. Garnish with fresh dill (optional) and serve with dill pickle relish on the side (optional).