Preheat the oven to 350 degrees and prepare a few baking sheets with parchment paper, or line with a silicone mat. Make the dough. In a large bowl or stand mixer, beat 1/2 cup + 1/3 cup butter for 2 minutes until smooth, scraping the sides and bottom a few times in between. This is one stick of butter plus 1/3 cup, you can just cut your stick of butter at the 1/3 cup line (see photos).
Add 1/2 cup butter flavored shortening, or regular shortening will do. (You can also replace this with butter, see note!) Beat well into the butter, trying to get out most of the lumps.
Add 1 cup white sugar and 1 cup packed brown sugar. Beat for another 2 minutes, taking the time to scrape the bottom and sides of the bowl in between. Your butter and sugar should be light and fluffy with no chunks of butter.
Add 2 eggs and 2 teaspoons vanilla. Beat well, scraping the sides and bottom of the bowl.
Add 2 cups whole wheat flour but don't mix it in yet (make sure you spoon and level your flour). Add 1 cup spooned and leveled all-purpose flour.
Use a small spoon (I use my teaspoon) to stir 1 and 1/4 teaspoons cinnamon, 1 teaspoon baking soda, and 1 teaspoon kosher salt into the flour. Gently beat the flour mixture into the butter mixture. Don't overdo it. There should still be flour streaks when you stop your mixer. Use a spatula to scrape down the edges of the bowl.
Chop 12 ounces of white chocolate. I like to have varying sizes of white chocolate, anywhere from the size of a dime to the size of a quarter. If you want, you can chop the remaining 4 ounces of white chocolate now and set aside (it's for pressing into the tops of the cookies. Or you can just toss it into the dough and mix it in! Either way.)
Add 12 ounces of white chocolate to the cookie dough and beat it in gently. Do not over mix the dough. You want all the flour streaks gone and to make sure all the ingredients are combined, but once that is done, stop mixing. Over mixing dough = tough cookies.
Use a large cookie scoop or a spoon to shape the dough. I like dough balls that are about 1 and 1/2 to 2 inches across (if you want smaller cookies, that's fine! Decrease the bake time.) Place cookie dough balls on the prepared baking sheet with about 2 inches in between them. I can usually fit between 8-12 cookies on an 11x17 baking sheet. If they are very large, do 8 cookies on a pan.
Bake the cookies at 350 for about 10-12 minutes, until the edges are a very light golden and the edges have set. It's ok if the centers of the cookies (no more than the size of a quarter) are still shiny. The rest of the cookie should be matte.
Shape the cookies. Immediately after taking the cookies out of the oven, use a spoon to push the edges of the cookies toward their centers. This makes the cookies round in shape and makes the center thicker and more chewy. You have to do this within 30-60 seconds of taking them out of the oven, before the edges harden. See my Chewy Chocolate Chip Cookies recipe for more details about this technique!
While the cookies are still warm, press the remaining 4 ounces of chopped white chocolate into the top of each cookie.
Remove the cookies to a wire cooling rack and let cool. But you better eat at least one warm. With milk. Live your best life!
Freezer instructions: You can freeze this dough and bake later! I like to shape the dough into balls and store them in a ziplock bag. They will keep in the freezer for up to 3 months. I never thaw cookie dough before baking. Just bake straight from frozen and add a couple minutes to the bake time. Voila!