Whisk together flour, cinnamon, nutmeg, and allspice. In a large bowl, with an electric mixer on medium, beat butter, sugar, egg, and vanilla until smooth.
On low speed, beat in flour mixture until blended. Knead by hand 1 minute. Divide dough into quarters. Wrap each piece in plastic and refrigerate 2 hours.
Heat oven to 350°F. Put oven racks in middle. Grease two baking sheets. Lightly coat interiors of molds with oil, including all crevices. Lightly dust with flour; tap out excess. (Molds must be dusted before each new cookie is formed; do not re-oil.) Divide each piece of dough into 3 equal portions. Using 1 portion to fill each mold, work dough into the form. Press firmly to remove air pockets. Use the side of your finger to remove excess dough from the edge of the mold.
Rap the mold against a wooden surface to loosen cookies, then place on baking sheet 1 inch apart.
Bake 15 minutes, until golden brown on edges. Transfer sheet to wire rack and let stand 5 minutes. Transfer cookies to wire rack to cool completely.
Cookie tiles, also known as Speculaas mold, are sold by Sweet Celebrations, 888-328-6722 and Brown Bag Cookie Art, 800-392-8893.