Preheat the oven to 400° F and line a baking sheet with parchment paper.
Add 1 teaspoon of olive oil to a pan and place over medium high heat. Add the shallots and cook for about 5 minutes, until they become fragrant and begin to brown. Add the mushrooms and ½ teaspoon salt, and cook, stirring occasionally for about 10 minutes. The mushrooms should have released their liquid and begun to brown. Add the arugula to the pan and give everything a quick stir to allow it wilt. Remove from heat and set aside.
While vegetables are cooking, mix together the tofu, nutritional yeast, lemon juice, water or stock, garlic, and ½ teaspoon salt in a food processor fitted with an s-blade. Process until the mixture is thick and looks like ricotta cheese. This could take several minutes, and you may need to stop and scrape down the sides of the food processor once or twice. Add more water or stock if the mixture is too thick. Set aside until ready to use.
To make the crust, Line a baking sheet with a piece of parchment paper. Lay down one sheet of filo dough on top of it. Keep the rest of the filo sheets covered with a clean, wet kitchen towel to avoid drying out. Quickly brush the sheet with a thin layer of olive oil using a pastry brush. Layer another sheet on top of it, and brush that one with a thin layer of olive oil. Continue this step until all of the sheets are layers and brushed with oil.
Gently fold the edges of the dough inward. Brush with a small amount of olive oil to help keep it in place.
Spread the tomato sauce evenly over the filo crust.
Dollop the tofu ricotta over the crust.
Gently spread the vegetable mixture over the crust.
Bake for 20 – 25 minutes, or until the crust is golden brown.
Slice and enjoy! Serve hot.