Preheat oven to 350 degrees F.
To make crespelle, sift flour into a bowl. Crack eggs into bowl and beat, adding milk a little at a time until all is incorporated. Allow to rest 30 minutes.
To make the filling, heat olive oil in a 8-inch saute pan until smoking. Add onion and saute until soft, about 5 to 6 minutes. Add radicchio. Saute until soft, about 5 to 6 minutes, and pour mixture into a bowl. Stir in goat cheese, balsamic vinegar and parsley and set aside.
Heat a 6-inch non-stick pan until hot and brush with olive oil. Turn heat down to medium and pour 1 1/2 tablespoons batter into pan. Cook until pale golden, about one minute, and flip. Continue the process until all the batter has been used, yielding between 8 to 10 crespelle. Fill each crespella with 2 tablespoons goat cheese mixture and fold in half. Continue filling all crepes until all crepes are full. Be sure to leave 4 tablespoons goat cheese mixture for topping.
Butter bottom and all sides of 10-inch by 8-inch ceramic baking dish. Lay filled crespelle overlapping in baking dish. Smear remaining goat cheese mixture over top and place in oven until piping hot and crispy on top, about 12 to 15 minutes. Remove and serve with a raw radicchio salad.