Mix flour, salt, and baking soda in a small bowl and set aside.
In a medium pot, add butter over medium heat and cook until melted. Turn heat down to low.
Cook, and whisk occasionally, until milk fats seperate out and slightly burn on the bottom of the pan. Little brown specks will appear and it will smell very nutty, about 15 minutes.
Let brown butter cool for a few minutes then add sugars and stir to combine. Let cool for a few more minutes until warm.
Add sugar/butter mixture to a stand mixer bowl or a bowl with a hand mixer and cream together on medium speed until slightly fluffy and combined, about 5 minutes.
Add egg and yolk, vanilla, half and half, and lemon juice.
Next add flour in a few batches and stir on low speed until well incorporated. Don’t overmix though.
Stir in chocolate chips. Cover and store in the fridge for at least an hour, but you could store it for up to a week.
When ready to bake, preheat oven to 350. Add large tablespoons of dough to a parchment sheet lined baking sheet. Roll dough into balls.
Bake for 9-10 minutes. Preferably underbake these.
Cool for a minute or two preferably on a wire rack and eat as soon as possible!
Notes
Note: If you want to bake these cookies right away, chill the brown butter and sugar as you cream it together by cooling it in a bowl in an ice bath. It will chill down and then your dough will be cool enough to use right away, although you'll still get best results by resting the dough for at least an hour.