In small frying pan, melt butter over medium heat and cook until amber browned, swirling the pan occasionally. Immediately remove from heat and pour into heat-safe bowl.
In large bowl, mix together the egg, milk, 3 tablespoons brown butter, yeast and sugar until combined. Add the salt and nigella seeds. Gradually add the flour, one cup at a time, stirring with each addition.
Turn the dough onto a lightly floured surface and knead for 7 to 10 minutes. Clean out the bowl and pour remaining oil in bowl and grease the bowl. Add the dough, flipping to coat with oil. Cover with a clean kitchen towel or plastic wrap and place in a warm place to rise for 1 ½ hours.
Grease a springform pan with 1 tablespoon of brown butter.
Divide dough into 4 equal balls. Reserve 2 tablespoons of brown butter for each dough ball and working one dough ball at a time, lightly grease countertop and hands with brown butter. Using palms of hands, stretch the dough ball into a thin rectangle, sprinkling more brown butter as needed to help stretch the dough until it's almost see through, approximately 12 x 20 inches. Drizzle remaining brown butter over dough and carefully roll up the dough lengthwise like a cinnamon roll, to form a long rope.
Cut the dough rope into 4 equal pieces and place in springform pan. Continue until all the dough is arranged. Cover with a clean kitchen towel or plastic wrap and place in a warm place to rise for 30 minutes. Note: After 20 minutes, pre-heat oven to 375 degrees Fahrenheit.
Bake for 35 to 40 minutes or until golden brown.
Cool for 15 minutes. Serve and enjoy with eggs, grated tomato salsa and zhoug.