In a mixing bowl, beat the butter, sugar, and vanilla until creamy and smooth. Stir in the flour and then beat until well mixed. Turn the dough out onto a large piece of plastic cling film, wrap it tightly, and refrigerate for 1 hour.
Preheat oven to 350°F.
Roll the dough out to 1/4-inch thick on a floured surface. Flour the top of the dough so it doesn’t stick to the rolling pin. Use cookie cutters to cut simple shapes, or roll the dough into a large rectangle and cut it into smaller rectangles.
Place the cookies on a baking pan, spacing them 2 inches apart. Brush the dough with the egg and sprinkle almonds and coarse sugar over the top.