Preheat oven to 400 degrees. Prepare pie crust. Line a 9-inch deep dish pie pan with the bottom crust; set aside.
In a large saucepan, combine berries, sugar, salt, and lemon juice and zest over medium heat. Simmer until just warm, about 5 minutes.
In a small bowl, whisk together water and cornstarch until smooth. Gradually stir cornstarch mixture into berry mixture. Bring to a simmer and cook until thickened, about 5 minutes, stirring occasionally. Remove from heat and stir in the butter until melted.
Cool berry mixture for 15 minutes, then pour into to prepared pie crust. Add the top crust and crimp the edge. Brush top of pie with beaten egg and sprinkle with coarse sugar, if desired.
Bake for about 45 minutes, or until crust is golden and filling is bubbly. Place foil over the crust about halfway through cooking time, if needed, to prevent crust from overbrowning.
Remove pie to a wire rack to cool before slicing and serving.