Melt 1½ cups salted butter in the microwave at 20-second increments (do not overdo it!). Pour the melted butter into a large bowl and cool for 15 to 20 minutes. I found slicing the butter into tablespoons made for a more even melt.
Add 1½ cups light brown sugar and 1 cup granulated sugar to the butter mixture and mix with a hand mixer for 4 minutes.
Scrape down the sides of the bowl and add 1 large egg, 1 additional large egg yolk, and 1 tablespoon vanilla extract and mix for 30 seconds.
Add 2 tablespoons hot water to a small prep bowl with 1 teaspoon baking soda and stir to dissolve. Stir into the butter mixture with a rubber spatula.
In a separate bowl, add 2 cups all purpose flour, 1 cup cake flour, 1½ teaspoons salt, 1 teaspoon baking powder, and 1 teaspoon cinnamon and mix to combine. Add this mixture ½ cup at a time to the bowl, beating on low after each addition just until combined and scraping down the sides of the bowl as needed.
Fold in 1 cup Ghirardelli white chocolate chips and 1 cup Ghirardelli milk chocolate chips, as well as 1 cup pecan pieces, if desired, with a rubber spatula.
Using a medium cookie scoop, scoop the balls (1.5 tablespoons—about 1.1 oz. each) onto a parchment-lined baking pan. Stack the balls two high and chill for 1 hour before covering them with plastic wrap (the dough is soft and any pressure from covering could squish them). Refrigerate them for at least 3 hours, preferably 24.
Preheat the oven to 350°F and line a fresh baking pan or cookie sheet with parchment paper. Place the cookie dough balls on the baking pan, leaving 3 inches between scoops. I recommend baking no more than 8 cookies per 12x17-inch pan. Use two cookie pans to rotate batches, ensuring the pans have cooled before baking the next batch on them.
Press additional chopped pecans into the tops of the dough before baking. You don't want to do this after, like with the chocolate chips, because we want the pecans to toast and have a better flavor.
Bake for 11 to 14 minutes, rotating halfway through; most of the cookie will be golden (more so on the edges). If baking from frozen, bake for 12 to 15 minutes.
Swirl inside a large circular biscuit or cookie cutter or a plastic bowl to reshape them and help make them a little thicken.
Press additional chocolate chips into the tops of the freshly baked cookies. This gives them a more polished look (and extra chocolate!)
Let the cookies cool on the pan for about 5 minutes after swirling and adding chips before transferring to a wire rack to finish cooling.