Make the Cookies:

1. Preheat the Oven:
   Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat.

2. Mix Dry Ingredients:
   In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.

3. Cream Butter and Sugar:
   In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3 minutes.

4. Add Eggs and Vanilla:
   Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.

5. Combine Wet and Dry Ingredients:
   Gradually add the dry ingredients to the wet mixture, mixing until just combined. Stir in the milk until the dough comes together. The dough will be soft but not sticky.

6. Form the Cookies:
   Using a spoon or cookie scoop, drop rounded tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart.

7. Bake the Cookies:
   Bake for 10-12 minutes, or until the edges are lightly golden. Be careful not to overbake them—these cookies should be soft and slightly chewy.

Make the Butter Glaze:

8. Prepare the Glaze:
   While the cookies are baking, make the glaze. In a small saucepan, melt the butter over medium heat. Add the sugar and water and stir until the sugar dissolves completely. Bring the mixture to a boil, then reduce the heat and simmer for 2-3 minutes.

9. Add Vanilla:
   Remove the saucepan from heat and stir in the vanilla extract.

Glaze the Cookies:

10. Glaze the Cookies:
    Once the cookies are baked and slightly cooled, use a spoon or pastry brush to coat each cookie with the warm butter glaze. Allow the cookies to absorb the glaze for a few minutes before transferring them to a wire rack to cool completely.