In a medium saucepan, combine chopped apples, along with butter, flour, ¼ cup sugar, cinnamon, nutmeg, water, and lemon juice over medium heat. Cook, stirring occasionally for about 4-6 minutes until the apples are slightly softened.
Remove from heat and spoon apple mixture into a bowl. Cover and place in fridge to chill while preparing the rest of the ice cream.
Heat milk and remaining ¾ cup sugar in a medium saucepan over medium heat. Stir constantly, until the mixture just reaches the point of simmer. Remove from heat.
Lightly whisk egg yolks in a separate medium bowl. Pour about half of the warm milk into the bowl with the egg yolks, whisking while you do so. Pour the egg/milk mixture back into the saucepan with the rest of the milk. Cook mixture over low heat, stirring constantly, until it thickens enough to coat the back of the spoon.
In a separate medium-sized bowl, pour the heavy cream. Strain the egg/milk mixture into the heavy cream, making sure to continue to whisk. Stir in the vanilla. Cover with plastic wrap and place in the fridge for at least 4 hours.
Once mixture has been sufficiently chilled, process in ice cream maker according to manufacturer’s directions. When the ice cream is almost done hardening, mix in the apple mixture and cider caramel, making sure to reserve some of the caramel to drizzle over the finished ice cream.
Scoop ice cream in airtight containers and place in the freezer for another 4+ hours, but ideally overnight.
Serve ice cream in bowls with pie crust cookies and extra apple cider caramel drizzled over the top.