It helps to keep both the stamp and the dough very cold; and to flour the stamp lightly. After you stamp and have them on a cookie sheet (preferably lined with parchment or, better, Silpat), chill them a few more minutes before putting in the oven. This helps the dough to retain the imprint during the baking.
Don’t use a recipe that calls for softened or melted butter - cut the butter in as you would for pie pastry, and then knead it only lightly. Chill before rolling out and cutting/stamping.
Thank you × 100. Really helpful: )