How to make the sour cream that some restaurants serve with quesadillas?

There are many variants of sour cream. I am not quite up to date on the naming of dairy products in Belgium, but don't you find sour cream labeled as "zure room" (Dutch) or "crème aigre" (French)?

Mexican sour cream (Crema Mexicana) has however a higher fat content than the sour cream commonly available in European countries. A close approach is crème fraîche, but it might not be just as sour. If you want to make it yourself, you can add living bacteria culture (e.g. from yogurt) to heavy cream (fresh cream with >35% fat) and keep it at roughly 37°C until it reaches the required thickness.

If you're looking for American-style sour cream, which it looks like from your pictures, you would start with a light cream (roughly 20% butterfat content), and then add a culture containing lactic-acid bacteria, particularly Streptococcus lactis (and perhaps some other things like Leuconostoc citrovorum for flavor). Set this out at room temperature for 12-24 hours, until it thickens appropriately.

You may have trouble finding these exact culturing bacteria in Belgium. These cultures are easily found in the United States in "cultured buttermilk," which uses the same process and bacteria as sour cream production, except with milk instead of cream. As I discussed recently in an answer to another question, you should be able to find similar cultures in the German product Dickmilch. I don't know if a similar product is available in Belgium, but if so, it may be able to provide you with the correct bacteria to add to your light cream.

Again, this will produce American-style sour cream, which is my best guess for your situation based on the picture you provided.

(By the way, Tor-Einar Jarnbjo's recipe should also work. It will make a thicker and richer product, since it is using heavy cream, and will have different flavor notes, since the yogurt bacteria are active at different temperatures and produce slightly different byproducts. It's just another kind of cultured cream, which, from all I can tell from a photo, may be closer to the version you eat in Belgium. Also, note MandoMando's comment that it may be possible to use the sour cream from the restaurant itself as a starter.)

Mixing a couple of teaspoons of lemon juice or white wine vinegar into half a pint of cream will make a good approximation.

I have gastrointestinal conditions and a daily dose of cultured/fermented foods makes digestion easier for me. I'm also physically disabled so I try to keep things as simple for myself as possible. One way I achieve this is to put a dollop of a potently cultured sour cream on a lot of my foods. I even slather it on cornbread instead of butter. Taste delicious by the way.

This is how I achieve my super easy, thick consistency, extra tangy, potent sour cream the easy way. I blend in store bought Kefir and thick non flavored yogurt into a store bought thick consistency sour cream until I achieve the sourness that I like. (The more kefir you add - the more tangy tasting it becomes.) If the consistency becomes too thin for my liking - I add a teaspoon at a time - of name brand unflavored Gelita (instant gelatin powder that emulsifies in cool/cold ingredients while condensing into a thick viscosity.) I use a lot of sour cream so while I still have the remainder of the last the weeks batch - I make a new batch for the next week. Try one teaspoon of Gelita first, then return to refrigerate and leave overnight. If viscosity is still too thin - add another teaspoon and check tomorrow morning. Works like a charm without any undesirable, odd flavor undertones. Walla !!!! Super easy, extra tangy sour cream with no cooking !!!