Preheat oven to 350 degrees
Whisk together sugar, egg, vanilla extract, canola oil, and milk.
In separate bowl, mix together 3 cups flour, baking powder, baking soda, and salt.
Make a well in center of flour mixture and pour liquid ingredients into center.
Stir to combine until a slightly crumbly dough forms.
Add cranberries and white chocolate chips. Stir until cranberries and chips are just mixed throughout.
Form dough into a smooth ball, adding more milk as needed.
Place dough onto a well-floured surface and roll out until dough is 3/4 inch in thickness.
Dip cookie cutter into flour to ensure cutter doesn't stick and then cut dough into cookies.
Place cookies onto sheet pan and bake for 10-12 minutes until just golden on sides and bottom. While cookies are baking, make icing.