Whisk the flour, salt and baking powder together and keep close by.
Working in a mixer with the paddle attachment, if you have one, beat the butter at medium speed for a minute or so, until it is smooth. Still beating, add the sugar and continue to beat for about 2 minutes, until the butter is light and pale. Add the egg and the yolk and the vanilla and beat another minute or two. Reduce the mixer speed to low and steadily add the flour mixture, mixing only until it has been incorporated. In fact, because this dough is best when worked least, you might want to stop the mixer before all the flour is thoroughly blended into the dough and finish the job with a rubber spatula. When mixed, the dough will be soft, creamy and appealingly malleable.
Turn the dough out onto a counter and divide it in half. If you want to make roll-out cookies, shape each half into a disk and wrap in plastic. If you want to make slice-and-bake cookies, shape each half into a chubby sausage (the diameter of the sausage is up to you - I usually like cookies that are about 2 inches or more across) and wrap in plastic. Whether you're going to roll or slice the dough, the packets must be chilled for at least 2 hours.
Getting ready to bake the cookies: Center a rack in the oven and preheat the oven to 350 degrees F. Have two lined baking sheets at the ready. For these, I prefer to bake a single sheet at a time. You can fill both sheets and keep one sheet covered in the refrigerator while you bake the other.
If you are making slice-and-bake cookies, use a ruler to mark off 1/4-inch intervals on each roll of dough. With a sharp thin-bladed knife, slice the dough into rounds and place the rounds on one of the baking sheets, leaving about 1 1/2 inches of space between each cookie.
If you are making roll-out cookies, work with one packet of dough at a time and roll the dough between sheets of plastic wrap or wax paper to a thickness of 1/4 inch, lifting the plastic or paper and turning the dough over often so that it rolls evenly. Lift off the top sheet of plastic or paper and cut the cookies - I like a 2-inch round cookie cutter for these. Pull away the excess dough, saving the scraps for re-rolling, and carefully lift the rounds onto the baking sheets, leaving about 1 1/2 inches of space between each cookie. (This is a soft dough and you might have trouble peeling away the excess or lifting the cut outs. If so, cover the dough, chill it for about 15 minutes and try again.) After you've rolled and cut the second packet of dough, you can form the scraps into a disk, chill, roll, cut and bake them.
Bake the cookies, one sheet at a time, for 9 to 11 minutes, rotating the sheet at the mid-point. The cookies should feel firm, but they should not color much if at all. Remove the pan from the oven and dust the cookies with sugar or cinnamon-sugar, if you'd like. Let them rest 1 minute before carefully lifting them onto a rack to cool to room temperature.
Storing: The cookies will keep at room temperature in a tin for up to 1 week.
Freezing: Well wrapped, the dough can be refrigerated for up to 3 days or frozen for up to 2 months.