1. Heat oven to 350 degrees . Combine caramels and half-and-half in a small saucepan. Cook over medium-low heat, stirring occasionally, until caramels are melted, about 8 minutes. Cool slightly.
2. In a large bowl, beat butter and sugar until fluffy, about 3 minutes. Beat in egg and salt, then cooled but still fluid caramel mixture. On low speed, mix in flour. Add some dough to cookie press. Press cookies out onto ungreased baking sheets. Bake at 350 degrees for 10 minutes, until set and just beginning to brown around bottom. Transfer to wire racks to cool and repeat with remaining dough.Glaze
3. In a small saucepan, combine sugar and half-and-half. Heat over medium-low heat until sugar is dissolved. Place wire rack with cookies over a baking sheet. Drizzle with glaze and sprinkle with salt. Let cookies dry until glaze is set before stacking or storing.