Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
For the Cookie Dough:
2. In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
3. In a large bowl, beat the softened butter, granulated sugar, and brown sugar until creamy and smooth.
4. Add the egg and vanilla extract, and beat until well combined.
5. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

For the Filling:
6. Using a small cookie scoop or spoon, scoop a tablespoon of cookie dough and flatten it slightly in your hand.
7. Place a teaspoon of cherry pie filling in the center of the flattened dough.
8. Scoop another tablespoon of cookie dough and flatten it, placing it on top of the cherry filling. Seal the edges of the cookie dough together to completely enclose the filling. Repeat with remaining dough and filling.

Place the stuffed cookie dough balls on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 12-15 minutes, or until the edges are lightly golden. Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
For the Glaze:
11. In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.
12. Drizzle the glaze over the cooled cookies.