Cook the pasta in enough boiling salted water until al dente.
Divide radicchio into leaves and cut them lengthwise into strips about 2 cm wide.
Remove the skin from the garlic clove and chop very finely. Heat olive oil in a frying pan, sauté garlic and radicchio for about 3 minutes, season with salt and pepper. Add milk and goat cheese. Let goat cheese melt while stirring.
Drain the pasta and mix with the radicchio-cheese sauce.