Preheat a medium non-stick skillet. Preheat the oven to 400F.
Cut the dough into 4 equal portions. Dust your hands with flour and spread the dough into 4 rounds, 8-10 inches each.
To the hot skillet, add 2 tablespoons of EVOO, the sliced mushrooms and 2 cloves of chopped garlic. Cook the mushrooms until they are dark and tender, 10 minutes, then season with rosemary, salt and pepper.
In a bowl, mash the beans with the spinach and remaining clove of garlic, a drizzle of EVOO and salt and pepper, to taste.
On each round of dough, spread 1/4 of the bean mixture on one half of the dough. Top with 1/4 of the mushrooms and then about 1/2 cup of cheese. Fold the dough over and seal the calzones by pressing the edges lightly. Brush a cookie sheet with EVOO and arrange the calzones on the sheet. Brush each calzone lightly with EVOO. Bake the calzones until golden all over, 15 minutes.
Heat the pizza sauce over low heat in a small pot.
Serve the calzones with small ramekins of pizza sauce alongside for dipping.