03Bake cookies until almost firm in center, 12 minutes. Cool on sheets 2 minutes, then cool on racks. Repeat, using all dough. Do ahead Store airtight at room temperature up to 3 days or freeze up to 2 weeks.
04Bring first 2 ingredients to simmer. Cover; chill 5 hours. Strain. Place powdered sugar in bowl. Whisk in half and half by spoonfuls until glaze is spreadable. Frost cookies; decorate. Let stand until glaze sets. Do ahead Store between sheets of waxed paper in airtight container at room temperature up to 3 days.