1. Preheat oven to 425 degrees Fahrenheit (220 degrees Celsius).
2. Place mushrooms on a baking sheet. Drizzle with olive oil and sprinkle with salt and pepper. Place in oven and roast for 20 minutes.
3. Raise oven heat to 475 degrees Fahrenheit (240 degrees Celsius). Divide the pizza dough into four to five pieces and shape into circles. Roll out the circles on a baking sheet, stretching at the corners. Brush with olive oil and poke holes in the dough so it doesn’t puff up.
4. Place in oven and bake for 20–25 minutes. (Alternately, you can make the pizza doughs in a skillet. Bring the skillet to high heat with about one teaspoon of oil. Place the rounded, stretched-out pizza dough in the skillet. Fry on either side until fully baked and some char spots appear on the dough.)
5. While the pizza is baking, combine the pesto sauce ingredients in a small bowl. In a separate bowl, combine the ingredients for the quick-pickled onions.
6. Remove the baking pan from oven and immediately brush the pesto sauce over the dough, reserving the extra pesto for the tahini dressing. Top the dough with the lettuce of your choice. Sprinkle with roasted mushrooms, sliced cherry tomatoes, pickled onions, avocado slices, and feta.
7. Combine the remainder of the pesto dressing with the tahini paste and lemon juice. Drizzle dressing over the top of the pizza and serve.