To Make Dough: In a small bowl, dissolve yeast in water. Add the oil, sugar and salt; mix in 1 cup of the flour until smooth. Gradually stir in the rest of the flour, until dough is smooth and workable. Knead dough on a lightly floured surface for about 5 minutes, or until it is elastic. Lay dough in a bowl containing 1 teaspoon olive oil, then flip the dough, cover and let rise for 40 minutes, or until almost doubled.
To Make Filling: While dough is rising, combine the ricotta cheese, Cheddar cheese, pepperoni, mushrooms and basil leaves in a large bowl. Mix well, cover bowl and refrigerate to chill.
Preheat oven to 375 degrees F (190 degrees C).
When dough is ready, punch it down and separate it into 2 equal parts. Roll parts out into thin circles on a lightly floured surface. Fill each circle with 1/2 of the cheese/meat filling and fold over, securing edges by folding in and pressing with a fork. Brush the top of each calzone with egg and place on a lightly greased cookie sheet.