Thoroughly wash the arugula, then pat it dry with a clean kitchen towel. Crumble the goat cheese with a fork until easily spreadable.
In a large bowl, combine the all-purpose flour, yeast, sugar, and salt. This will form the base of the naan dough.
Add the yogurt, lukewarm water, and olive oil. Mix to combine, then knead until a smooth, elastic dough forms.
Knead for at least 10 minutes. If the dough is too sticky, add a little flour, but be careful not to make it too stiff.
Cover the dough and let it rise in a warm place for 1 hour, or until doubled in size.
Divide the risen dough into 6 equal portions. Shape them into balls, then roll each into an oval shape.
Spread one half of each rolled-out naan with a portion of the goat cheese, then sprinkle with the dried arugula leaves. Fold the other half over, press gently, and then roll out slightly again.
Heat a skillet over medium heat and cook the naans for 1-2 minutes per side, until golden brown spots appear.
Brush the cooked naans with melted butter while still warm – this enhances the flavor of the dough and gives it a glossy finish.
Serve fresh – it goes well with salads or as a stand-alone dish.
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