Start by peeling and roughly chopping your garlic clove, then rinse and roughly chop your basil leaves. Zest your lemon half using a microplane before you juice it, since it's much easier to zest a whole lemon half than a squeezed one. Set everything near your food chopper so you're not scrambling mid-process.
Add the chopped garlic, basil, dijon mustard, Worcestershire sauce, mayonnaise, lemon juice, lemon zest, salt, and black pepper directly into your small food chopper or processor bowl. There's no particular order that matters here, so just toss it all in together.
Pulse or blend the mixture until the garlic and basil are finely minced and everything looks fully combined and creamy. This usually only takes about 20 to 30 seconds. Scrape down the sides once if needed to make sure nothing's stuck.
Give the dressing a quick taste before serving. If it needs more brightness, add a touch more lemon juice; if it needs more punch, a small pinch of extra salt or pepper does the trick. Adjust in small increments since the flavors are already fairly concentrated.
Transfer the dressing to a jar or airtight container and let it sit in the fridge for at least 15 to 20 minutes before serving. This short rest lets the garlic and basil flavors settle into the mayo base rather than tasting sharp and separate.