In a medium bowl whisk together flour, cornstarch, baking powder, baking soda, and salt. Set aside.
In a large bowl, with the mixer on medium-low speed, beat melted butter with white and brown sugar, until the mixture is smooth.
With the mixer on low speed, add eggs one at a time.
Add vanilla and honey, and beat just until combined.
With the mixer on low speed, gradually and the flour mixture, stirring until fully combined.
Using a spatula, stir in chocolate chips.
Cover the bowl with plastic wrap and chill in the fridge for 30 minutes or overnight.
When ready to bake, preheat oven to 350 degrees F (175C) and cover 2 cookie sheets with parchment paper.
Scoop about 2 tablespoons of dough and roll into balls, arrange onto the prepared cookie sheets 2 inches apart as they will spread.
Bake about for 8-9 minutes for smaller cookies or 10-13 minutes for larger cookies. Cookies are done when the edges are golden-brown but will appear still a bit underdone on the outside.
Remove from oven, cool on the baking sheet for 5-7 minutes, than transfer to a cooling rack. If desired, press a few more chocolate chips into the hot cookies.
Make sure to let the cookies sheets cool, before placing any remaining dough on them. Also, keep in the fridge any leftover dough.