Preheat oven to 375°.
Combine Pie Filling ingredients: Combine apples, lemon juice, butter, 3 tablespoons arrowroot starch, 1 teaspoon cinnamon, salt, and vanilla paste. Set aside.
Make Caramel: Combine brown sugar and Swerve (or sugar) in a medium saucepan. Heat over medium-high heat until sugar melts. (Brush mixture off of sides of pan with a wet pastry brush, if needed.) Cook sugar until fragrant and caramel colored, being careful not to burn it. Remove from heat; add cream carefully and stir (if may pop a bit). Melt in butter and salt.
Remove parchment off the top of one of the pie crust doughs. Flip pie dough carefully into pie plate, removing other parchment, and press against sides of pie plate to fit, leaving a bit of an overhang of crust to ultimately meet with top crust. Add apples on top of pie dough in pan. Press apple gently to pack a little bit. Carefully pour caramel over apples.
Remove parchment off the top of the other pie crust dough. Flip pie dough carefully on top of apples, removing other parchment. Pinch bottom crust overhang with top crust to seal edges of pie. Pierce pie with a skewer to create a few holes to vent. Brush top of pie crust with lightly beaten egg.
Place pie on a jellyroll pan with short sides. Pull out a large enough piece of aluminum foil to reach all of the way around the pie. Fold foil in third lengthwise. Wrap long piece of foil all of the way around the pie to support the crust a bit.
Bake pie at 375° for 60-70 minutes, or until pie is cooked and bottom is lightly browned (if you're using a clear pie crust! :)).
Allow pie to cool. Dig in.