1. Preheat oven to 350 degrees (175 C). Line 2 baking sheets with baking paper (parchment paper). Do not greese the paper or cookies will spread.In a medium bowl, combine all-purpose flour, cake flour, baking powder and baking soda and set aside.In a thick-bottomed skillet, melt half of the butter over medium heat. Continue cooking, whisking frequently, for about - 1 to 3 minutes or until butter is lightly browned and has nutty aroma. Be careful not to burn the butter.
2. Transfer to a large bowl and add remaining unmelted butter. Stir until combined. (If your butter melts completely, put it in the freezer for a few minutes until it has consistency of a firm yogurt or cream).
3. Add honey, brown sugar, white sugar, salt and vanilla.
4. Whisk (with a hand whisk, no mixer needed) until incorporated.
5. Add egg and yolk and continue whisking until mixture is smooth. If you want your cookies to have cracked surface, let the mixture stand for 10 minutes at this point.Using wooden spoon or rubber spatula, stir in flour mixture until just combined. Do not overmix. Stir in chocolate chips.Take 2 tablespoons of dough at a time and roll into balls.
6. Place 2 inches apart on lined baking sheets. You can add more chocolate chips on top of each cookie to make them look pretty (optional).
7. Bake 1 sheet at a time on the middle rack, until cookies are puffy and slightly brown, about 10 to 12 minutes (depending on your oven). Cookie centers should still be soft. Rotate baking sheet halfway through baking. Cool the cookies on the sheets.