Cream butter and sugar. Add corn syrup and eggs and mix well.
Add the flour, salt, cinnamon, ground ginger, and cloves, and mix well. Add the oatmeal and mix well.
To easily chop the crystallized ginger, pulse in a food processor or blender. Be careful not to overdo it, or your ginger will become mushy and clump together. Alternately, you can just chop it with a knife. After chopping, add the crystallized ginger to the cookie dough and incorporate throughout.
Using a small cookie scoop, place the dough on un-greased cookie sheets, stoneware, or cookie sheets lined with baking mats. Bake at 350 degrees for about 10 minutes, or until bottom edges are barely browned.
Remove from oven and press lightly with a glass dipped in sugar. (You can make the sugar stick to the glass by spraying the bottom with cooking spray before your first "press." Dip glass into sugar for each press. You should not need to spray the glass again).
Put cookies on wire racks to cool.
Cream butter and cream cheese. Add vanilla and mix until smooth. Add powdered sugar until desired consistency is reached.
When cookies are cool, spread between two cookies.