Set your oven to 300 degrees and line a baking sheet with parchment paper. Scatter the chopped pecans on the paper in an even layer. Toast them in the oven for 7 minutes and stir them, rearranging them on the pan. Return the pan to the oven and bake them for another 7 minutes. Turn off the oven and set the nuts aside.
In a large bowl using a hand mixer or in the bowl of an electric stand mixer, beat the butter for 40 to 60 seconds on medium speed until it is smooth and creamy.
Add the white sugar and the brown sugar, beating these ingredients together until they are fluffy and light-colored. Add the eggs and vanilla extract, turning the mixer up to high speed, scraping down the sides of the bowl as needed.
In a separate, medium-sized bowl, stir together the flour, cornstarch, baking soda, and salt until combined.
Take the bowl of dry ingredients and mix them into the other bowl of wet ingredients on low speed with the electric mixer. This dough will be very thick and stiff.
Add the pecans, mixing with the mixer on low for just a few seconds, just until combined and the nuts are evenly distributed in the cookie dough.
Cover the bowl with aluminum foil or plastic wrap and chill the dough for at least 4 hours or overnight. You can reserve it in the refrigerator for up to 3 days.
When the time is up, turn your oven on and set it to 350 degrees. Line your baking sheets with parchment paper.
Remove the dough from the fridge. Put the ¼ cup of granulated sugar in a small bowl. Use a cookie scoop or a tablespoon to scoop out blobs of cookie dough, rolling them into walnut-sized balls with your hands. The balls may be slightly crumbly but will come together as you handle the dough balls and press them together.
Next, roll the dough balls in the granulated sugar and place them on the parchment-lined baking sheets about 2 inches apart.
Bake the cookies in the preheated oven for 11 to 13 minutes, just until they are lightly browned around the edges.
The baked cookies will still look undercooked in the middle, but that is okay. Just let the cookies sit on the baking pans for about 5 minutes. If they are too puffy, press the cookies down in the center, very gently, using the back of a spoon.
Scrape the cookies off the pan with a spatula and place them on wire racks to cool. When the cookies are completely cool, store them in an airtight container for up to a week.