Chai Caramel Apple Pie

Name: Chai Caramel Apple Pie
Cuisine: European, British
Ingredients: 360g all purpose flour; 260g unsalted butter; 4 tbsp granulated sugar; 120-180ml ice cold water; 1/2 tsp of salt; 150g granulated sugar; 60ml water; 2 tbsp corn syrup; 2 cinnamon sticks; 3 cloves; 160ml heavy cream, warmed; 60g unsalted butter; 1 tsp vanilla extract; 1/2 tsp salt; 5-6 apples (honeycrisp, gala, pink lady); 2 tbsp cornstarch; 60g dark brown sugar; juice of 1/2 lemon; 2 tsps ground cinnamon; 2 tsps vanilla extract; 1/4 tsp salt; 1 egg; 1 tbsp water