Make the filling: Heat a large skillet over medium-high heat. Add the oil and then add the onion, cook for a minute or so, and then add the broccoli. Cook for 3-5 minutes or until tender and bright green. Season with salt and pepper and set aside.
Make the galette: Preheat the oven to 375°F (190°C). Line a baking sheet pan with parchment paper.
On a floured surface, roll the disk out to a circle about 12 inches (30-cm) in diameter. Gently transfer the dough onto the prepared sheet pan.
Put the broccoli mixture and grated cheese in the center of the dough circle. Spread out to within about 2 inches (5-cm) of the outside edge. Fold the edge of the dough over the filling, creasing and folding until completing the circle. Brush the crust with the egg wash or heavy cream.