Preheat your oven to 500°F if using a baking sheet, or to its highest setting if using a pizza stone or steel. If using a stone or steel, place it in the lower third of the oven before preheating. Allow the oven to heat for at least 30 minutes, then switch to high broil just before baking.
In a large skillet over medium-high heat, melt the butter. Add the mushrooms along with a generous pinch of salt and a few cracks of black pepper. Sauté for 3 to 5 minutes, or until the mushrooms soften and begin to release their moisture. Remove from the heat and transfer the mushrooms to a paper towel-lined plate to absorb any excess liquid.
Roll or stretch the pizza dough into a 12- to 14-inch circle. Transfer it to a baking sheet or pizza pan, or to a floured pizza peel if using a stone or steel.
Spread the marinara sauce evenly across the dough, leaving a ½-inch margin around the edges. Layer on half of the sautéed mushrooms, followed by the mozzarella cubes. Scatter the remaining mushrooms over the cheese. Sprinkle the shredded parmesan (or chosen cheese) evenly over the top and season with a light touch of salt and pepper.
Transfer the pizza to the hot oven and bake until the crust is golden and crisp and the cheese has developed lightly browned spots—8 to 10 minutes on a baking sheet, or 6 to 8 minutes on a stone or steel.
Once baked, remove the pizza and, if desired, finish with a drizzle of olive oil and an extra pinch of sea salt. Garnish with chopped fresh chives. Let the pizza rest for a few minutes before slicing and serving.