For the cookies: Position a rack in the lower third of the oven and preheat the oven to 350 degrees F. Line two cookie sheets with parchment paper.
Sift together the flour, baking soda, cinnamon, salt, allspice and cloves in a medium mixing bowl and set aside.
Cream the butter and both sugars in the bowl of a stand mixer fitted with a paddle attachment (or a large mixing bowl if using a hand-held mixer) on medium speed until light in color, 3 to 5 minutes. Add the eggs and vanilla, and beat until fluffy, 1 to 2 minutes. Mix in the oats until just combined.
Add the dry ingredients in thirds until just combined, for no more than 2 minutes. Sprinkle in the toasted coconut and raisins and stir until just combined.
Scoop the dough onto the prepared cookie sheets with a large ice cream scoop, leaving 1 inch between each cookie to ensure even baking. Lightly tap down each cookie with the palm of your hand and sprinkle with just a pinch of turbinado sugar. Bake for 8 to10 minutes in the middle of the oven, rotating the sheet half way through the baking time for even doneness.
For the filling: Cream the butter on medium speed until light and fluffy, 2 to 3 minutes. Add 1 cup of the confectioners' sugar, milk and vanilla, and mix on low speed until smooth and creamy, 1 to 2 minutes. Add the second cup of sugar while mixing on low speed until the filling reaches the desired light and fluffy consistency, 2 to 3 minutes.
To sandwich the cookies: Put a dollop of filling (about 1 tablespoon) on the bottom of one cookie and place the other cookie right side up on top. Repeat with the remaining cookies.