Preheat the oven to 375°F (190°C).
In a medium bowl, mix flour and salt together.
In a separate large bowl, beat together chilled butter, granulated sugar, and brown sugar until creamy.
Add the beaten egg and vanilla extract, mixing until smooth.
Gradually mix the dry ingredients into the wet mixture until just combined.
In another bowl, toss together diced apples, cinnamon, nutmeg, lemon juice, and cornstarch.
Fold the apple mixture into the cookie dough gently.
Scoop tablespoon-sized mounds of dough onto a lined baking sheet, spacing them about 2 inches apart.
Bake for 12-15 minutes, or until the edges are lightly golden.
Let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.