Prepare the toppings: Slice the baby bella mushrooms. Heat the olive oil in a small skillet. Saute the mushrooms and fennel seeds for about 3 to 5 minutes, until they become golden brown and start to release moisture. Add 3 pinches kosher salt and continue to cook a few minutes. Remove from the heat.
Bake the pizza: When the oven is ready, dust a pizza peel with cornmeal or semolina flour. (If you don’t have a pizza peel, you can use a rimless baking sheet or the back of a rimmed baking sheet. But a pizza peel is well worth the investment!) Stretch the dough into a circle; see How to Stretch Pizza Dough for instructions. Then gently place the dough onto the pizza peel.
Spread the pizza sauce over the dough using the back of a spoon to create a thin layer. Add the mozzarella cheese. Top with the mushrooms, peppers, red onion, and feta cheese crumbles. Sprinkle with dried oregano and a few pinches of kosher salt.
Use the pizza peel to carefully transfer the pizza onto the preheated pizza stone. Bake the pizza until the cheese and crust are nicely browned, about 5 to 7 minutes in the oven (or 1 minute in a pizza oven). Slice into pieces and serve immediately.