Preheat the oven to 350 degrees F (175 degrees C).
In a large bowl or bowl of a stand mixer, cream together 1/2 cup of butter and white sugar until smooth. Beat in the eggs one a time, mixing well after each one. Combine the flour, baking powder, allspice and cinnamon; stir into the batter until blended. The dough will be very stiff.
Roll the dough out on a lightly floured surface to 1/8 to 1/4 inch thickness. Cut into circles using a juice glass or cookie cutter. Place 2 inches apart onto ungreased baking sheets.
Bake for 10 minutes in the preheated oven, or until the edges start to brown lightly. Cool cookies on wire racks for at least 15 minutes.
While cookies cool, make the frosting. Beat the butter and salt together until soft, then gradually mix in the confectioners' sugar and vanilla until smooth and light.
Spread strawberry jam onto one side of a cookie, then top with another cookie to make a jam sandwich. Spread frosting on top, and place a maraschino cherry half in the center before the frosting sets. Repeat with the remaining cookies.
