Preheat oven to 400°F.
Dice butter into cubes and put back in the refrigerator. Place flour and salt in a food processor and pulse until combined. Add butter and pulse until the butter is crumbly, just a few seconds. Add 3 tablespoons apple cider and run the food processor until the mixture starts to clump. Test the mixture with your fingers - is it crumbly or smooth? If it’s too smooth to form one full ball in the food processor add 1 teaspoon more of apple cider (up to 1 full tablespoon more) until the mixture forms a ball when the processor is running. Be careful not to add too much liquid.
Divide the dough into two balls. If the dough is too soft, chill for 30 minutes before rolling it out. If you can, roll out each ball separately on a lightly floured surface. (A silicone mat is very helpful for this step!) The diameter of the crust should be at least 1” larger than an inverted pie plate. Place one pie crust in a 9” pie plate. Place the other on a cookie sheet covered with parchment or wax paper. Chill both crusts until the filling is ready. (The chilling is important. They MUST be chilled before adding filling, topping, and baking for optimal results.)
Place the apples and 1 1/2 cups of apple cider in a large skillet. Cover and cook over medium heat, stirring often, until the apples are almost translucent, about 5-7 minutes. Remove the apples and reserve the cooking liquid in the pan.
Stir together granulated sugar, 1 tablespoon cornstarch, and salt. Stir in 2 tablespoons of cold apple cider. Add the cornstarch mixture to the hot apple liquid in the pan. Cook over medium-low heat until the mixture thickens, about 5 minutes. Add the butter and stir until melted. Remove from heat and add the apples back to the hot liquid. Let cool for 5-10 minutes.
Remove crusts from the refrigerator. Slice the flat crust into 1” slices using a knife or pizza cutter. Sprinkle the brown sugar, cinnamon and remaining 1/2 teaspoon cornstarch in the bottom of the pie crust in the pie plate. Place the slightly cooled apples into the pie plate. Top the pie with the strips of dough in a lattice pattern.
To create the lattice pattern (see this post for image tutorial): choose every other strip and place them on the pie crust with 1” gaps between them. Then take each remaining strip, starting at one end of the pie, and weave the strips over and under the strips that are on the pie in an alternating pattern.
Brush the top of the pie with a little heavy whipping cream and sprinkle with granulated sugar. Place the pie on a cookie sheet and bake for 30-40 minutes until the crust is golden brown. Cool completely before cutting. Serve with ice cream or whipped cream and apple cider syrup.