Preheat the oven to 375°F. Grease and lightly flour the baking sheets.

In a medium bowl, whisk together the flour, oats, baking soda, salt, ginger, cinnamon, and allspice; set aside. In a large bowl, using an electric mixer on medium speed, cream the butter and sugar together until fluffy. Beat in the eggs, one at a time. Mix in the treacle and/or molasses. On low speed, add about one third of the flour mixture at a time, alternately with the milk, mixing until blended.

Drop teaspoonfuls of dough 2 inches apart on the baking sheets. Bake in the center of the oven for about 12 minutes, or until a cookie springs back when lightly touched (like a baked cake). Let the cookies cool on the baking sheet for a few minutes, then transfer to a wire rack to cool completely.

Prepare the treacle cream filling. Spread a 1/4-inch layer of filling on the bottom side of a cookie and top immediately with a similarly sized cookie, with the bottom side touching the filling. Repeat with the remaining cookies. Wrap cookies individually in plastic wrap if you plan to store them in layers or travel with them, because they tend to cling together. Wellwrapped cookies may be frozen.