In a small bowl, combine honey, arrowroot, and spices; set aside. In a large bowl, toss apples with lemon juice. Add honey mixture; toss to coat.
Line a 9-in. pie plate with bottom crust; trim even with edge. I poke holes in crust for ventilation. Fill with apple mixture; dot with butter. Roll remaining crust to fit top of pie; place over filling. (You can also do lattice work for a pretty top.) Trim, seal and flute edges. If you have a rolled out crust, cut slits in crust.
In a small bowl, beat egg white until foamy; brush over crust. Sprinkle with cinnamon and sugar if desirable. Cover edges loosely with foil.
Bake at 375° for 25 minutes. Remove foil and bake until crust is golden brown and filling is bubbly, 20-25 minutes longer. Cool on a wire rack.
The pies (uncooked) freeze well if you prefer to make them ahead of time and serve later. I just thaw them in the refrigerator the day before I bake them. I hope you enjoy making these with your family!