The subject of engine break in is, unfortunately, shrouded in mystery and controversy, both inside and outside the scooter world. It's very difficult to quantifiably say that one engine break-in method works better than another. There are basically two schools of thought, though: take it easy, and ride it like you stole it. Rather than tell you which one is correct, we'll present both and let you decide for yourself.
Take It Easy
The "take it easy" approach says that, for a modern Vespa, the first 625 miles (about 1000km) should be ridden using no more than three-quarters of the throttle, avoiding jackrabbit starts, and taking pains to vary your RPM. The theory here is that there are a lot of close-tolerance parts in the engine, and when the engine is new, those parts haven't necessarily worn together yet. Taking it easy gives those metal parts a chance to seat themselves to each other and avoids generating so much friction that something in the engine gives out.
After the first 625 miles (and the all-important first service), it's generally considered safe to ride at full speed without worrying about RPM or anything else.
Dealers almost universally instruct new buyers to follow this break-in method, although their motivation in doing so probably has more to do with avoiding breakdowns and angry buyers than producing the most amount of horsepower.
Ride It Like You Stole It
The "ride it like you stole it" method says that for the first 20 to 50 miles you should thrash your scooter within an inch of its life. This includes climbing steep hills at wide-open throttle, freeway riding, and as much stress on the engine as you can manage. After the initial thrashing, immediately change the oil (you'll notice a superfine metal particulate suspended in the oil) and then ride it like normal. Or like you stole it. Your choice.
This break-in method is based on the idea that cylinder bores are given an initial cross-hatch pattern when the engine is machined so that the piston rings will hone themselves down to the exact tolerance of the bore. This, in turn, will provide a better seal, higher compression, less blow-back, and less burned oil. You've only got 20 or so miles of riding, though, before the cross-hatch pattern is gone.
Proponents of this break-in method claim that you end up with a faster, more powerful engine thanks to this break-in method.
The general consensus is that the engine of a modern Vespa will loosen up a bit after 1,000 to 2,000 miles, getting smoother and even a bit stronger in the process.
Regardless of which engine break-in approach you take, the single best thing you can do for your scooter is to change the oil regularly, and use only a high-quality synthetic oil.
The "ride it like you stole it" method mentioned above is factually incorrect in some areas and does not list the full and proper way to undertake this task. Additionally, this 'fast run-in' method is rather an internet trend that potentially could have unfortunate and unexpected consequences for folks who use it as described above. This method is normally reserved for racing engines and some commercial engines and aircraft, with bigger component clearances on key engine parts so that excess heat doesn't cause any damage during the carrying out of this process. To use this method and correctly apply it requires considerable skill and the knowledge to know whether or not the engine in question is suitable for this type of run-in procedure. Not all engines are and some can be damaged considerably if you do this to them. Since the inception of the "fast run-in" technique some time ago, empirical and other engineering evidence suggests many owners lack the skill, knowledge and experience to carry out this run-in procedure correctly. As a result this racing type run-in procedure is not universally recommended for owners with road going bikes or recommended by manufacturers and remains the domain only of certain websites who will tell you it's ok to do this to your expensive motorcycles or scooter. It should be noted and in contradiction to the article above, that one aim is to retain as much of the 'cross-hatch pattern on the cylinder wall
as possible. Once an engine loses this cross-hatch pattern the cylinders are damaged (called cylinder glazing) and the engine life will be very short lived since there is nothing to retain the oil on the cylinder walls. This leads to poor lubrication, poor piston and ring seal with the cylinder walls, poorer power output, high oil use, and often broken piston rings early in the life of the engine.