Using the paddle attachment, beat the butter until smooth and creamy. Add the sugars and corn syrup. Mix until light and fluffy.
Add the egg and mix. Add the flour and vanilla. Mix until combined.
Gather the dough and divide depending on how many colors you want. Add a few drops of the gel food coloring on each and mix. Shape each dough into a large disc. Wrap in cling film and refrigerate for an hour.
Preheat the oven at 350°F/175°C
Line 2 baking sheets with parchment paper.
Roll out dough between 2 sheets of parchment papers to 1/8-inch thickness for 2-inch cookies and 1/4-inch for larger 4-inch cookies
Using a cookie cutter, cut out cookies and transfer to prepared cookie sheets, spacing 1 inch apart.
Bake 1 sheet at a time for 10-12 minutes for 2 inch cookies or 12-14 minutes for 4 inch cookies or until the cookies are firm on top and golden around edges.
Allow to cool on cookie sheet for 5 minutes before transferring to cool completely on cooling racks.
For the filling
Roll out the fondant to just over a quarter of an inch thickness and cut into circles using the same cookie cutter as for the cookies.
Brush one side of the fondant with a little milk and press this onto the bottom of one cookie.
Brush the other side of the fondant with a little water and place the bottom of a second cookie, pressing gently to secure the sandwich
Notes
This dough Can be made 2 days ahead and kept chilled in the refrigerator until needed.