I also add fresh cooked bacon (NEVER bacon bits) and capers.
A yolk, a tsp of dijon, pepper, little salt, juice half a lemon, couple dashes of Worcestershire, couple anchovy filets, half a garlic clove.
Blend homogenous with a stick blender. Then slowly blend in a stream of neutral oil; get it to mayonnaise consistency. Taste and adjust (probably wants pepper). Then: back it out to dressing consistency with water (or lemon juice) a tsp at a time. [†]
Knobs (do any/all/none): grate pecorino or parm, just a bit, into the dressing in the first stage. Double, triple, or quadruple the anchovies. Add some white wine vinegar along with the lemon juice. Microplane the garlic (careful, will really amp the garlic). Before thinning back to dressing consistency with water, add some extra virgin. Pinch of MSG.
If you're being hardcore (ie date night), before you start the dressing, fill a ziploc with ice and put it in your salad bowl, and put your serving bowls in the freezer. Also hardcore: use half as much garlic, and make up the difference with 2x as much garlic confit.
Don't do the thing where you build the dressing on the salad (like, cracking an egg into the bowl or whatever). It's a parlor trick, not a way to dial in the ideal Caesar. Also don't bother with the "rub the garlic into the salad bowl" thing; just makes it harder to dose the garlic.
Extra tip: freshly roasted brussels sprouts love Caesar dressing. (Roasted brussels sprouts love any bright high-fat sauce; Caesar is just the platonic ideal.)
Keeps about a week in the fridge, but each time you use it, refresh the acid (just a splash or lemon juice or vinegar).
(I make a lot of Caesars).
Take a step back and see a Caesar as an anchovy vinaigrette, and then you can immediately vary it to different settings --- lime instead of lemon, add some chile (or aji amarillo), tortilla instead of croutons, fresca instead of parm.
[†] You can also just blend neutral oil in until you get the dressing consistency you want; theoretically you'll get a better texture and a little more flavor concentration this way, but I think the win is marginal vs. being able to knock this dressing out mechanically without thinking hard about it, and you can just dial up the flavors a bit beforehand if you're worried.
(And customizable - I usually make mine with a little more garlic. This last time I tried making it with a whole-grai. Mustard and the results were delightful.)