This is a slight variation on Alton Brown's "The Chewy" recipe. I've used this recipe for a while and have made couple tiny alterations which I have included here. I switched to dark brown sugar while the original recipe cals for light brown sugar. The darker the sugar makes for chewier cookies which I like. I also scaled back the amount of chocolate chips a little because I like the basic cookie a lot and don't want it to be hidden by too many chocolate chips.
Melt the butter in a 2-quart saucepan over low heat. Set aside to cool slightly.
Sift together the flour, salt and baking soda onto a paper plate. (I don’t sift these ingredients anymore. I put them in a bowl and whisk them together briefly to add air to the flour. That seems to be enough and less messy.) Pour the butter into your stand mixer's work bowl. Add the sugar and brown sugar and beat with the paddle attachment on medium speed for 2 minutes.
Meanwhile, whisk together the whole egg, the egg yolk, milk and vanilla extract in a measuring cup. Reduce the mixer speed and slowly add the egg mixture. Mix until thoroughly combined, about 30 seconds.
Using the paper plate as a slide, gradually integrate the dry ingredients, stopping a couple of times to scrape down the sides of the bowl. (I carefully spoon the four mixture in from the bowl about a third at a time until it’s all combined.) Once the flour is worked in, drop the speed to "stir" and add the chocolate chips. Chill the dough for 1 hour.
Preheat the oven to 375 degrees F and place racks in the top third and bottom third of the oven. (I only bake one sheet at a time on the middle rack.)
Scoop the dough into 1 1/2-ounce portions onto parchment-lined half sheet pans, 6-8 cookies per sheet. Bake 2 sheets at a time for 15 minutes (I bake them 13.5-14 minutes. 15 was too long for my oven.), rotating the pans halfway through. (Not necessary if you only use one sheet at a time.) Remove from the oven, slide the parchment with the cookies onto a cooling rack and wait at least 5 minutes before devouring.