1. **Preheat:** Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper.

2. **Cream Butter & Sugars:** In a large bowl or stand mixer, cream the softened butter, granulated sugar, and brown sugar together on medium-high speed for 3–4 minutes until light and fluffy.

3. **Add Wet Ingredients:** Add the egg, honey, and vanilla extract. Beat until fully combined, scraping down the sides of the bowl.

4. **Mix Dry Ingredients:** In a separate medium bowl, whisk together the flour, cornmeal, cornstarch, baking powder, and salt.

5. **Combine:** Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until no flour streaks remain. Do not overmix.

6. **Scoop:** Use a large cookie scoop (about 3 tablespoons) to portion the dough. Roll into smooth balls and place them on the baking sheets, spaced 3 inches apart. Gently press down on the tops just slightly to flatten.

7. **Bake:** Bake for 11–13 minutes. The edges should be set and slightly golden, but the centers should still look soft and puffy. Do not overbake.

8. **Cool:** Let the cookies cool on the baking sheet for 10 minutes (they will firm up), then transfer to a wire rack to cool completely.

9. **Make Topping:** While cookies cool, whisk together the 4 tablespoons softened butter, honey, powdered sugar, and pinch of salt until creamy and smooth.

10. **Serve:** Dollop or pipe the honey butter mixture onto the center of each cookie. Serve at room temperature or slightly warm.