Combine yeast, warm water and sugar in a small bowl, cover with plastic wrap and allow to stand in a warm place for 10 minutes or until small bubbles appear on the surface.
Meanwhile, combine sifted plain flour and salt in a large bowl. Pour in oil and yeast mixture and stir until a dough has formed. Turn dough onto a lightly floured surface and knead for approximately 5 minutes or until dough is smooth and elastic.
Place dough in a large lightly greased bowl. Cover with plastic wrap and let rise in a warm place for 40 minutes or until dough has doubled in size.
Divide the dough into 4 and roll each piece out on a lightly floured board into 20cm rounds.
Combine shredded BBQ chicken, mushrooms and Leggo’s Pesto and place a quarter of the mixture on one side of each of the dough rounds. Top filling on each calzone with 6 halves of bocconcini cheese and 3 basil leaves torn into pieces. Brush edges with beaten egg, place other half of dough over filling and gently seal the edges.
Place calzones onto two baking paper lined baking trays and brush with remaining beaten egg and sprinkle with black pepper. Bake in a preheated oven at 190°C for 15-20 minutes. Serve with tomato relish.