This coffee mostly known as Turkish Coffee (Turk Kahvesi / τούρκικος / קפה טורק / török kávé / Kafe turke / cafea turcească etc...),
"Greek Coffee or Turkish Coffee" as an ingredient: it's roasted coffee and grinder set to "0", it's finer than espresso (1) and moka espresso machine (2), and filter coffee (3). however you can not grind coffee fine like this at Starbucks, but you can grind yourself at home, finest it's gets more aromatic becomes the coffee, since you didn't filter it, the coffee will always stay at the bottom.
by the way, middle roasted coffee is great for turkish coffee. even in some countries they are using golden roast and espresso roast.
and for best result; try to drink without sugar.