These keep for several days in an airtight container. You can make the dough in advance and freeze it, too. (Chill it in the refrigerator until firm enough to handle, and then form into a log about 12 to 14 inches long. Wrap well in a double thickness of waxed paper, twisting the ends closed, and freeze. Then, when you want cookies, slice off pieces with a sharp knife, adding about 2 minutes to the total baking time.)
Preheat oven to 325 degrees F. Melt the butter over low heat and set aside to cool. Put oven racks at the top and lower-middle positions. Stir together the flour, baking soda, and salt in a small bowl and set aside.
In the large bowl of an electric mixer, on low speed beat together the butter and both sugars until thoroughly blended. Beat in the egg, egg yolk, and vanilla. Add the dry ingredients, and on the lowest mixer speed beat until just combined. Fold in the chocolate chips.
Place large scoops of dough (about 2 tablespoons per scoop) onto parchment-covered cookie sheets, about 8 or 9 scoops per sheet. (If you donot have baking parchment, grease the cookie sheets; the cookies will end up slightly more crispy on the bottoms.)
Place one cookie sheet on each oven rack. Bake for 6 to 8 minutes, then reverse positions of the cookie sheets. Bake for another 6 to 8 minutes, until just barely golden brown and puffed. Remove from the oven and let cool on the cookie sheets for about 10 minutes before removing to wire racks to cool completely. Repeat for remaining cookie dough.