Preheat oven to 475°F.
Place dough on a work surface; drizzle with 1 Tbsp. oil, turning to coat. Stretch out to a 10″ round.
In a large cast-iron skillet over medium heat, cook sausage, breaking it up into small pieces with a wooden spoon, until browned. Add the mushrooms and cook these until just starting to soften. Transfer the sausage-mushroom mixture to a bowl.
Remove the skillet from heat and carefully lay the dough inside (making sure to create an almost 2-inch lip). Season with salt, layer in the smoked gouda cheese, then spread marinara over the entire bottom. Add, in layers, the sausage-fennel mixture, fennel, roasted red peppers, and another thin layer of marinara. Top with mozzarella cheese. Sprinkle with dried basil.
Transfer skillet to oven and bake pizza on top rack until crust is golden brown around the edges and cheese is browned in spots and bubbling all over 15-18 minutes. Let cool for 10 minutes.
Cut into hearty wedges and enjoy.