Heat apple juice in the microwave in a microwave-safe bowl in 30-second intervals until very warm, but not boiling. Add chai tea bags, cover, and let steep for 10 minutes. Discard tea bags.
Meanwhile, peel and chop apples, tossing them in a bowl with lemon juice to keep from browning.
Combine cinnamon, ginger, cloves, cardamom, and black pepper for spice blend in a small bowl.
Combine apples, apple juice-chai tea blend, the spice blend, brown sugar, butter, maple syrup, vanilla extract, and salt in a large pot. Cook over medium heat, stirring frequently, until the apples start to soften, about 30 minutes.
Transfer 1/4 cup of the warm apple liquid from the pot to a small bowl. Add cornstarch and whisk until completely dissolved into the liquid and no clumps remain. Stir mixture back into the pot. Continue cooking over medium heat, stirring often, until the mixture starts to thicken, about 5 minutes. Pour the filling into a bowl and set aside to cool, about 1 hour.
While filling cools, preheat the oven to 425 degrees F (220 degrees C).
Pour filling into one of the thawed pie crusts and press the other crust dough over the top. Cut a small, shallow slit in the top with a sharp knife. Gently brush beaten egg over the top crust. Cover the outer edges of the pie with aluminum foil to avoid burning.
Bake in the preheated oven for 30 minutes. Gently remove foil and continue to bake until golden and bubbly, about 15 minutes more. Allow to cool until the pie is warm, but not hot, before serving.