How do I prepare arabic coffee in a stone Dallah?
This is the result of experimentation with Daniele's answer and the resources of a normal Australian household.

Be prepared with a tea towel or other holding-item. Marble has a huge thermal inertia and insulation is a decadent western invention.

On the other hand electric kettles are awesome.

First: Wash everything thoroughly. I boiled a couple litres of water and poured them through the dallah. I then washed everything with soap and hot water, then rinsed with more boiling water. This told me two things: 1) The marble can handle boiling water. (Which was likely... but good to test), and 2) I wasn't going to be drinking any marble dust. 

Then, from a good coffee shop that roasts their own beans, get very very very finely ground coffee. Their espresso blend is a good start. While single origin can be better, it requires fine-tuning to find the right single-origin for this taste, especially as...

Buy a satchet of cardamom. If you're going to do true Jordanian coffee (instead of Saudi or Turkish) it's a function of which spice you combine. I've heard of cinnamon and saffron also being acceptable, but the "everyday" spice is cardamom. This is where single-origin will get you if you choose a bean that isn't compatible.

Now here is where I cheated. I've got an electric stovetop (boo, hiss... rental apartment. I kind of have to deal with it unless I want to ask a colleague for a bunsen burner.) I also own an electric kettle. I boiled water in the kettle, then measured 250 mils into the dallah, which I placed on a "hob" on my electric stove. I then turned the stove to medium. 

After about 5 minutes of watching, the marble was very warm, but the water never boiled. Technically, this is a good thing. I then added 2 heaping 
"standard" scoopfuls (about 20 grams, the scoop that comes with a bodium french press) of coffee mixed with about half a scoop of cardamom. I let that sit on the stove for 4 minutes, stirring the coffee every minute until the crema recombined. 

Pour (holding it with a tea-towel) gently into the marble tinytiny cups. 

I have to take mine with a few dollops of condensed milk because my word this coffee is strong. Good, but strong.