Beat the butter and sugar together in a large bowl, till light and fluffy. Beat in the egg and the extracts and the lime zest. Sift together the flour, corn-starch and the salt. Mix this in till you have a smooth dough. Do not overwork the dough.
If the dough seems crumbly and dry, add a little milk, a tbsp. at a time, just enough to form a dough. Do not add too much so it becomes sticky. Shape into a ball and wrap in cling film. Refrigerate for at least 4 hours or overnight.
When ready to make the cookies, turn out the dough onto a lightly floured work surface. Sprinkle a little flour on the dough (not too much or you’ll have tough cookies) as well. Knead the dough gently so it is pliable. Divide the dough into 2 or 4 pieces. Work on one piece and keep the others covered and in a cool place.
Roll the dough out to about a 1/8 inch thickness. If you do this on a piece of baking parchment, the cookies will be easier to lift off and transfer to the baking sheet. Dip your cookie cutters in flour and cut out cookies. Transfer the cut out cookie dough to ungreased or parchment lined baking sheets.
Place the scraps on top of each other and roll out and cut cookies. Repeat with remaining dough.
Bake the cookies at 180C (350F) for about 10 to 15 minutes till they start browning on the edges. Cool completely and transfer to an airtight tin till ready to decorate them.