Bring vegetable stock to a simmer in medium pot. Keep at a simmer, covered, over low heat.
Cut radicchio into shreds. Heat 1 tbsp olive oil in a pan over medium heat. Add radicchio, season and simmer for 15 mins. Add a splash of wine or water when it starts to dry out.
Heat olive oil over medium heat in a large saucepan. Add onion and sauté for 5 mins. Add rice and cook, stirring constantly for 3 mins.
Add wine, stirring until wine is completely absorbed by rice.
Add one cup of stock at the time to rice and cook. Stir constantly and wait until stock is completely absorbed before adding the next.
Keep rice at a constant simmer. Reduce heat to medium-low if mixture starts to boil.
After 10 mins add cooked radicchio. Stir well and continue adding stock until rice is just tender to the bite.
Season with salt & pepper to taste.
Once rice is cooked remove it from heat and stir in squacquerone cheese, butter and fresh parsley. Cover with lid and let the risotto rest for 2 mins before serving.