Hi,
So, I have a La Pavoni and I'm using it mainly for double espresso / cappuccino in the morning. Sometimes I would like an espresso (not double) but every time I try using the single basket I get horrible coffee. Did someone find a solution to this issue?

I've never used the single basket.

But I just split the shot with the double spout portafilter!

There are several ways to get terrible espresso with the La Pavoni single basket.

In the first place if one fail to use a large enough dose the tamper will hit against the sloped side before the dose is tamped at all or before it is tamped toward the centre. Make sure that there is enough untamped coffee so that when it is placed in the basket it is level across the top. This takes about 8 grams. Otherwise tamp as usual.

The normal double basket output from a La Pavoni is between 35 and 40 grams when the machine is properly bled, and when the group is at the correct temperature. You thus need to pull a shot with about 17-18 mL (or grams, espresso is near unit density). The easiest way to do this is to use a glass espresso cup and put 18 grams (mL) of water into it before ever making single shots. One can take a piece of tape and put it on the outside of the glass to mark the target amount. If you always use the same cup you will quickly learn the proper depth without the tape after making singles a while. You can do this with other cups, but you will need to use greater care. Too long a shot will be bitter as usual.

If you have a bottomless portafilter, use it for at least the first few shots. Especially watch the way that the first espresso appears when pulling the handle down. Watch it from a low enough vantage point to see the screen as the pull starts. You want to be sure you are getting an even tamp and distribution.

Watch the level of espresso in the glass cup as you pull it. When it gets to the tape, release the handle, remove the cup and put a waste cup under the portafilter and empty the rest of the group water into the waste container.

I think the La Pavoni single basket is designed in Italy for Italian style espresso. 6.5g-8g load and about 25-30g out. If you are interested in using Italian espresso blends with Italian dosing you'll probably have a good shot. American style espresso is a wholly different shot, and you'll need to adjust your parameters. RPavlis's description above will give you a starting point for playing around with different shot styles.

Thank you for your advice.
I do think maybe I put too little coffee. I used 7g with a 51mm basket (La Pavoni Millennium) and I suspected channeling...
I'll try to updose a little and see if it creates a better tamp and coffee.

I use 15.5 to 16 grams of coffee in my bottomless portafilter and usually get pretty good shots. I find the first and second shots are the best. If I'm doing three the third shot can be a little off. I also find tamping pressure can make a difference. At first I was tamping with a lot of pressure but now it's around 10 lbs and a polish. I also try to do less pressure with each successive shot. I think it makes a difference. Then there's group head temperature, the grind, the bean...it's endless.

Just wanted to update and say thank you. Actually, updosing my single basket to 8g improved my singles a lot. Although, still far from my double shots level, but it is much better than before (and drinkable )

Practice. Singles are quite doable when you get in the zone.