Proof the yeast. In a medium bowl, dissolve the yeast and sugar in the warm water. Let sit for about 5 minutes until bubbly.
Mix. Whisk the flour and salt in a large bowl. Mix the yogurt, melted butter, and egg yolk into the yeast mixture. Stir the yogurt mixture into the flour until mostly combined. Using an electric mixer with dough hooks (or a stand mixer), knead on medium-high speed for 5 minutes. The dough may be slightly sticky but smooth.
Let rise. In a warm location, let rise for an hour.
Divide the dough into 4 balls.
Roll out. On a well-floured surface, roll out the dough balls to 6 mm (1/4 inch) thickness. You can stack the rolled-out dough on a plate, with wax paper or parchment paper between each piece if your dough is still sticky.
Grill. Heat a grill pan over medium-high heat. If you do not have a lid for your pan, prepare some aluminum foil to place loosely over the pan. Place your pita dough in the pan, however many fit without touching, and cover either with a lid or foil. Cook until puffy and nicely browned on each side, about 1 ½ minutes per side. (See note for outdoor grill)
Stack the pitas while cooking the remaining breads.