Mix graham cracker crumbs with melted butter, sugar, and salt until it resembles damp sand. Press firmly into a 9-inch pie dish. Refrigerate for 15 minutes.
Blend hulled strawberries until smooth. Strain through a fine mesh strainer if desired for a silkier puree.
Beat softened cream cheese until completely smooth, 2 to 3 minutes.
Add condensed milk and beat on low until combined. Add strawberry puree, lemon juice, lemon zest, and vanilla. Beat until uniformly smooth and pink.
Whip cold heavy cream with powdered sugar to firm peaks. Fold gently into the strawberry mixture in three additions.
Pour into the chilled crust and smooth the top. Cover with plastic wrap and freeze for a minimum of 5 hours or overnight.
Before serving, whip cold heavy cream with powdered sugar and vanilla to medium-soft peaks. Spread or pipe over the frozen pie.
Top with sliced fresh strawberries and mint leaves. Slice with a warmed knife wiped dry between each cut. Serve immediately.