Cream butter, sugar, nutmeg and salt until light and fluffy. Beat in egg, egg yolk, rum extract and vanilla until well blended. Gradually add flour to butter mixture; blend thoroughly.
Cover dough and refrigerate at least 1 hour (or overnight.)
Preheat oven to 350°F.
Scoop out 1-inch sized balls of dough. Roll each piece with hands into 6 to 8-inch long, pencil shaped strip. Twist into pretzel shape by crossing one side of the strip to the middle forming a loop and then crossing the other side over the first loop forming a second loop. Place about 1-inch apart on a lightly buttered baking sheet. Brush the tops of the pretzels with the egg white then sprinkle with coarse sugar.
Bake 12 to 15 minutes or until lightly browned. Transfer cookies to wire racks; let cool. Store in airtight canister.