Bake the Pillsbury pie crust according to package directions, then allow it to cool completely on a wire rack. This step can be done ahead of time, or while you prepare the filling, since the crust needs to cool anyway before filling.
Hull and halve all 2.5 lb of strawberries. Divide them into two equal portions—place one half in a bowl and set aside for later. In a medium saucepan, combine the other half of the strawberries with the granulated sugar, 1/4 cup water, and fresh lemon juice. Bring the mixture to a boil over medium-high heat, then mash the strawberries with a potato masher or fork to break them down and release their juice. I like to leave some texture rather than making it completely smooth—this adds a nice contrast to the pie.
Once the strawberry mixture is boiling, reduce the heat to low. In a small bowl, whisk together the cornstarch with the remaining 1/4 cup water until completely smooth—this prevents lumps from forming in your filling. Slowly pour the cornstarch slurry into the simmering strawberry mixture while stirring constantly. Continue simmering for about 5 minutes, stirring occasionally, until the filling becomes glossy and thickens noticeably. Remove from heat, stir in the vanilla extract and salt, then let cool for 10 minutes.
Pour the cooled cooked strawberry filling from Step 3 into the bowl containing the reserved fresh strawberry halves from Step 2, folding gently to combine while keeping the fresh berries intact. Pour this beautiful filling mixture into the cooled pie crust from Step 1, spreading it evenly. I find that gently folding rather than stirring vigorously keeps the fresh strawberries looking beautiful throughout the pie.
Refrigerate the filled pie for at least 3 hours until the filling is completely set and the pie holds its shape when sliced. You can prepare this ahead and chill it overnight if convenient.
Slice the pie into wedges and serve each piece with a dollop of homemade whipped cream with a splash of vanilla. The cold, creamy whipped cream complements the fresh, jammy strawberry filling perfectly.