In a large bowl or the mixer, mix 5 cups all-purpose flour, 4 teaspoons baking powder, 1 tablespoon salt and 1 teaspoon sugar.
In a medium bowl mix ½ cup plain yogurt, 1 egg, 1 ½ cups warm water and ¼ cup olive oil. Mix and pour into a well in the flour mixture.
With the dough hook start mixing at low/medium speed, until a smooth dough forms that sticks around the hook, about 5 minutes. If it is too wet, add a tablespoon of extra flour. If making by hand, integrate the ingredients inside the bowl and then knead until smooth.
On a floured counter, divide the dough into 10 equal portions.
Form buns and put them on a plate dusted with flour.
Lightly brush the surface of each with olive oil, cover with loose plastic, and let rest for 1 hour.
Divide each bun into two parts.
Flatten half of the dough portions, and put 1 tablespoon of pesto in the center, spread it a little without breaking the dough, and put a piece of cheese on top.
Cover with another piece of dough, joining the edges well and taking care that the filling does not escape.
Turn on the skillet or grill, brush it with olive oil and add the bread.
Cook slowly over low heat until the dough is dry and the loaves are golden brown.
Repeat on both sides, allowing time for the dough to cook well.
Eat right away.