Activate the yeast.
In a large bowl, combine the warm water and yeast. Let stand for 5–10 minutes, until the yeast begins to foam.
Make the dough.
Add the flour and salt. Mix and knead by hand or with a stand mixer fitted with a dough hook for 7–8 minutes, until soft and elastic.
The dough should feel slightly tacky. If it is too sticky to handle, add flour 1 tablespoon at a time. If it feels dry or firm, add water 1 teaspoon at a time.
Let rise.
Lightly oil your hands and gather the dough into a ball. Place in a lightly greased bowl, cover, and let rise in a warm place for about 1 hour, or until doubled in size.
Divide and rest.
Gently press down the dough and divide into 2 equal portions for medium rounds, or leave whole for one larger pide.
Shape into balls and place on a parchment-lined baking tray, leaving room to expand. Cover and let rise for another 30 minutes.
Shape the pide.
Gently flatten each dough ball into a round about 1/2 inch thick.
Using lightly oiled or damp fingertips, press a circle around the dough, about 1 inch from the edge, to form a border. Press intersecting lines inside the circle to create a diamond or grid pattern. Press deeply without tearing through the dough.
Rest and preheat.
Let the shaped bread rest for 15 minutes. Meanwhile, preheat the oven to 450°F.
Brush and top.
If the pattern has softened during resting, gently press the lines again.
Brush lightly with egg wash or heavy cream, then sprinkle with the sesame and nigella seeds.
Bake.
Bake for 15–20 minutes, until golden brown and baked through. Begin checking a little earlier for smaller rounds; one large pide may take longer.
Let cool briefly before serving warm.