Put oven rack in middle position and preheat oven to 375°F. Line 2 large baking sheets with parchment or wax paper.
Whisk together flour, baking soda, and salt in a small bowl.
Beat together butter and sugars in a large bowl with an electric mixer at high speed until pale and fluffy, 2 to 3 minutes. Lightly beat 1 egg with a fork in a small bowl and add 1 3/4 tablespoons of it plus 2 remaining whole eggs to butter mixture, beating with mixer until creamy, about 1 minute. Beat in vanilla. Reduce speed to low and mix in flour mixture until just blended, then stir in chips.
Chill in the dough in the fridge for as long as possible, preferably 24 to 36 hours. If that is not feasible then chill for as long as possibe for beautifully browned cookies.
Scoop 1/4 cup batter for each cookie (I use an ice cream scoop), arranging mounds 3 inches apart, on 2 baking sheets. Flatten mounds into 3-inch rounds using moistened bottom of glass. I sometimes also add a pinch of salt to the top to make the chocolate zing. Form remaining cookies on additional sheets of parchment.
Bake, 1 sheet at a time, until golden, 13 to 15 minutes. Transfer cookies to a rack to cool and continue making cookies in same manner using cooled baking sheets.