Peel and slice peaches; be sure to remove and discard the core. (Here is a great method.) Toss with the sugar and lemon juice in a large bowl. Let sit for 30-45 minutes until juices release from the fruit.
Meanwhile, make the pie crust. Combine the flour and salt in a large bowl. Stir. Cut in shortening with a pastry blender or fork until small pea size pieces. Add the egg, vinegar, and water. Mix with your hands. Keep adding water, a little at a time, if needed, until the mixture is less crumbly and starts to come together. Empty the contents from the bowl onto the counter. Shape into a round disc. Wrap the disc in plastic wrap and CHILL DOUGH in the freezer for 15 minutes. This gives the dough time to rest and keeps the shortening from melting.
Once the dough has chilled, flour your surface and rolling pin. Unwrap dough and roll from the center outwards into a large circle about 1/4" thick. Transfer dough to pie dish. Form the dough as close the the sides and angles of the pie dish as possible. Leave a good 1/2" of crust over the edge, cut off any excess. Tuck the overlapping crust and crimp the edges.
Poke holes into the bottom of the crust with a fork. Place a piece of parchment paper inside the crust and fill with about 1/2 pound of dry beans (to use as weights). Bake at 350 degrees Fahrenheit for 20 minutes. Pull the parchment with the beans out of the crust. (Discard the beans or save them for future pies.) The bottom of the crust will look wet. Return the crust to the oven for 12-15 minutes to finish baking the bottom part of the crust. Cool completely.
Drain the peaches and reserve the juices. Juice should equal about 3/4 cup. If not, add water to reach 3/4 cup. Place 3/4 cup of juice, 1/2 cup of peach slices (about 1 peach), and 3 Tbsp of cornstarch in a blender. Blend until smooth. Place mixture into a small saucepan. Cook over medium heat until boiling and thick, whisking constantly. Remove from heat. Add 1 Tbsp butter, 1/2 tsp almond extract, and a pinch of salt. Whisk to combine. Cool slightly.
In the bowl of a stand mixer with the whisk attachment, beat the heavy cream and the powdered sugar until stiff peaks form.
Toss the peach slices with the cooled glaze and pour into the cooked pie shell. Top with whipped cream. For best results serve immediately. **Crust will absorb juices and soften, so don't fill the crust until ready to eat.**