Soften the butter.

In a bowl, beat the softened butter with sugar until fluffy.

Beat in vanilla extract and salt.

Stir in flour until just combined.

Place the dough between two sheets of waxed paper.

Roll out the dough to a 1/4 inch thickness.

Use 2 or 3-inch decorative cookie cutters to cut out shapes.

Place the cut-out shapes on parchment paper-lined rimless baking sheets.

Freeze the baking sheets for 10 minutes, until the cookie shapes are firm.

Preheat oven to 300F (150C).

Bake in the center of the preheated oven for 30-35 minutes, or until the cookies are firm to the touch and slightly golden around the edges.

Transfer the baked cookies to wire racks and let cool completely.

For the glaze, strain strawberry jam through a fine sieve into a large bowl to remove any pieces of strawberry.

Beat in the icing sugar.

Add 1 tablespoon of milk and the red food coloring.

Add up to 1 teaspoon more milk, if needed, to achieve a spreadable consistency.

Spread the glaze evenly over the tops of the cooled cookies.

Sprinkle the glazed cookies with coarse sugar.

Let the glazed cookies stand for about 4 hours, or until the glaze is completely set.