Put the flour in a bowl and add the salt. Stir well to combine. Make a well in the center and add the oil and half of the water while mixing until a very soft dough forms. Stop adding water as soon as the dough stops sticking to your hands. Knead on a lightly floured surface for 10 minutes or until soft and pliable. Shape into a ball and cover with a clean dish towel. Leave to rest for 30 minutes.
In a small saucepan, melt the butter over low heat and cook until it begins to brown. Remove from the heat and set aside.
Lightly flour your surface. Take walnut-sized pieces of the dough and roll into paper-thin circles. Cover half of the circle with the scallions, leaving a rim just under 1/2 inch (1 cm). Fold in half over the filling to form semicircles. Crimp or pinch the edges together to seal. Place on a clean dish towel dusted with flour and cover with another dish towel while you prepare the rest.
Place a heavy frying pan over low heat. It's hot enough when a drop of water thrown in it sizzles. Place a couple of the flatbreads in the pan and cook until the underside is dotted with brown spots. Turn over and cook the other side. Remove from the pan and place on a baking tray in a low oven to keep warm while you cook the rest of the flatbreads.
Reheat the brown butter and brush the kalāneh generously on both sides with it. Serve immediately.