Start by removing the large outer leaves from the head.
A head of puntarelle with a tagliapuntarelle bottom right
You will be left with an inner core of rather thick shoots—they look a bit like short, plump asparagus—and a few very slender leaves:
Cut off the tough base of this core and separate the shoots. Then push each shoot through the puntarelle cutter so as to produce little julienne strips. Or use a paring knife.
As you julienne the stalks, place them in a large bowl of ice water, along with the slender leaves. And when you're done, add more ice and let the puntarelle soak in the fridge for at least one hour.
After soaking, drain the puntarelle and pat them very dry.
Make the garlic and anchovy dressing
Place the garlic cloves in a mortar and grind them into a fine paste, then add the anchovy fillets and grind them, too, but not as fine.
Add the olive oil and then the vinegar, then mix well with a fork or whisk.
Finally, season with a bit of salt and freshly ground pepper.
Assemble your salad
Place a handful of puntarelle on a salad plate or in a shallow bowl.
Drizzle over dressing and serve immediately.
Notes
The puntarelle shoots can also be julienned with a paring knife, in which case trim off the solid base and cut the hollow tips with your knife.