Line a baking sheet with parchment paper. Beat together 1 cup of softened unsalted butter, 1/2 cup brown sugar, and 1/2 cup granulated sugar in a bowl until creamy, about 2-3 minutes.

Add 2 large eggs, 1/4 cup honey, and 2 teaspoons of vanilla extract. Mix until smooth, about 1-2 minutes.

Gradually sift in 2 cups of flour, 1 cup of cornmeal, 2 tablespoons of cornstarch, 1/2 teaspoon of salt, and 2 teaspoons of baking powder. Mix until just combined.

Cover the bowl with plastic wrap and chill in the refrigerator for at least 30 minutes.

Preheat the oven to 350°F (175°C). Scoop about 1/3 cup of chilled dough into balls and place them on the baking sheet. Bake for 13-15 minutes until golden around the edges.

In a bowl, combine 1/2 cup softened unsalted butter and 1/4 cup honey. Beat until creamy, then mix in 1 cup powdered sugar and 1 teaspoon vanilla until smooth.

Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack. Top with honey butter and drizzle with honey if desired.