To see who has liked your recipes (or other users' recipes), simply go to the recipe page in question and click on the number that appears below the like button. You will be taken to the Likes page, which will show everyone who has liked that dish.

You can also keep track of who you like through the notification center on the homepage, on the notifications icon, where besides the likes you can keep track of who saved your recipe, who started following you and who liked your dishes.