To make dough: In a large mixing bowl, place flour, baking powder, sugar, salt and olive oil. Stir together with whisk until texture is like that of moist cereal. Add egg and water and mix well with hands. Place on to floured work surface and knead like bread for 5 minutes. Cover and let rest 10 minutes.
To make filling: Place all ingredients in a large mixing bowl and mix well with hands.
Preheat oven to 375 degrees F.
Assembly: Roll out 3/4 dough to a 12 to 14-inch circle and place on a pizza peel, lightly dusted with semolina. Spread filling in center to within 3 inches of edge. Roll remaining dough into a thinner piece 10-inches in diameter and place over filling. Brush outer edge and top of center disk with cool water and fold outer edges inwards to meet center piece and cover the perimeter. Beat remaining egg and brush entire top. Score top with sharp knife in 5 places.
Slide on to stone in oven and bake for 40 minutes, until crust is dark golden brown. Remove and let rest 5 minutes before serving.