Heat oven to 350 F.
In medium bowl, use an electric mixer to beat together butter, sugar, salt, zest and mace until creamy. Mix in flour just until a dough comes together.
Scoop out dough in balls about the size of a walnut. Use the palms of your hands to flatten each ball into a round, then arrange on 2 baking sheets, leaving 1/2 inch between them.
Bake for 15 to 18 minutes, or until lightly golden brown. Makes 24 cookies. Cool completely on baking sheets. Store in an airtight container at room temperature for up to a week.