Step 1Separate the celery into stalks and wash them well, particularly the bottoms where the dirt loves to hide. Cut the celery into 2-inch matchsticks: Begin by cutting each stalk into 4-inch pieces. Cut each piece lengthwise into slender sticks. Gather a bunch of sticks together and cut them in half. Place the matchsticks in a bowl of ice water to freshen until you're ready to use them.
Step 2If the anchovies are salt-cured, rinse them well under cold water until they are soft and pliable. Remove any large bones or fins.
Step 3To make the sauce in a mortar, pound the garlic and the salt to a smooth paste; this will take about a minute. Start with a lesser amount of garlic and then add more as necessary. Add the anchovies and pound them to a paste as well. Add the vinegar and stir with the pestle until it is smooth. Gradually add the olive oil, starting with a thin stream, stirring with the pestle, until the sauce is smooth. Add a grinding of pepper.
Step 4To make the sauce in a blender, puree the garlic, salt, anchovies and vinegar until smooth. With the blender running, gradually add the olive oil, starting with a thin stream, until the sauce is smooth. You may have to stop once or twice and scrape down the sides to make sure the sauce is thoroughly combined. Add a grinding of pepper.
Step 5Dip a celery stick in the sauce and taste it. If you think it needs more garlic, mince another clove with a knife and add it to the sauce, grinding with the pestle or pureeing with the blender until smooth.
Step 6Drain the celery sticks and pat them dry with a paper towel. Place them in a salad bowl and add the anchovy sauce, starting with 2 tablespoons. Toss well to distribute the sauce equally among the sticks. Taste and add more sauce as needed. Serve at room temperature.