Into a bowl sift together flour, salt and baking powder. In a separate bowl with an electric mixer beat butter until creamy. Gradually add sugar, beating until mixture is light and fluffy. Add egg and vanilla and beat until combined well. Gradually add flour mixture, beating until mixture just forms a dough. Turn dough onto a sheet of waxed paper and form into an 8 X 2-inch log. Roll log in waxed paper and chill until firm, at least 2 hours and up to 5 days. (Dough may be frozen, wrapped in foil, for up to 2 months.) Keep dough chilled between batches and let soften slightly before cutting. Preheat oven to 350°F and lightly butter a baking sheet. Cut dough into 1/4-inch-thick slices and arrange about 1-1/2 inches apart on baking sheet. Bake cookies in batches in middle of oven until golden around edges, 10 to 12 minutes; transfer with a metal spatula to a rack to cool. Cookies may be kept in an airtight container at room temperature for 5 days.
Yield: About 30 cookies