Tortilla means something very different in Spain than it does in Mexico. The Spanish tortilla is actually a sort of potato omelette, which visually resembles a quiche. You could add any mushroom instead of the Agaricus arvensis, however this particular species has such a firm texture and rich flavor that it holds up extremely well in context. The trick is to pre-cook many of the ingredients before mixing them with the beaten eggs, then to cook it again all together to allow the eggs to firm up.
You can speed up the preparation time by partially cooking the potatoes in a microwave oven for a few minutes before slicing them, but this is not necessary. Crack the eggs into a large mixing bowl and beat them together with a fork. Mix the parsley, tarragon, paprika, salt and pepper into the eggs and set aside. Use a deep 10" nonstick frying pan, and individually sautée ingredients as follows. Using 1T of the olive oil, brown the onions for about 15 minutes on medium heat, stirring often, until brown. Set aside. Now sautée the potato slices in about 4T of olive oil for about 15 minutes (less if you use the microwave to precook them.) While the potatoes are cooking, be careful to keep them from sticking together, making sure they are all properly covered in oil and getting browned. They have a tendency to glue together during this stage if you don't work at it a bit. Set the cooked potatoes aside and sautée the chopped mushrooms and brocoli together for about 5 minutes (You might want to toss the brocoli into the pan after starting the mushrooms, to make sure it doesn't get overcooked.)
Now take all the pre-cooked ingredients and stir them into the mixing bowl with the eggs, covering everything completely with egg. You should have some olive oil left from the previous steps - spread about 1T of it around the pan, and wipe a bit more of it onto a large flat heat-resistant platter (to be used shortly.) Place all of the ingredients into the pan, arranging the potatoes so they lie flat. Cover the pan, and cook on medium heat for 3-4 minutes. Now remove the cover, place the oiled platter face down over the pan, and quickly invert the pan onto the platter. The tortilla should fall onto the platter upside down in one piece. Now slide the tortilla carefully into the pan again. Cook for an additional 3-4 minutes so as to brown the other side. Once again, invert the tortilla onto a serving platter and slice into pie-shaped wedges for serving. Serves 4-6 people as an entrée, more as an appetizer.