For Caesar salad dressing, a food processor merely minces the garlic, and a blender creates a dressing the consistency of a milkshake. Mashing the garlic in a mortar and pestle creates a smooth paste that makes the perfect base for this creamy dressing. (A bit of salt helps break down the garlic).
The good news is that if you don't have a mortar and pestle, you can still make a similar paste on your cutting board. Mince the garlic very finely and sprinkle it with coarse salt. Then repeatedly drag the flat side of the blade at the knife´s tip across the minced garlic to press into a paste, as shown. (If there´s a green sprout in the garlic, be sure to remove it first—it won´t mash well.) With a little diligence, you'll have a pretty good paste on your hands. Then you can mince the anchovies right on top of the garlic, scrape them both into a bowl, and continue whisking in the rest of the ingredients.