In a skillet over medium heat, melt 2 tablespoons of butter with an equal amount of olive oil. Add 2 finely sliced onions with a pinch of salt. Cook for 20–25 minutes, stirring occasionally, until the onions become golden brown and fragrant.

Preheat your oven to 400°F (200°C). Slice 2 medium sweet potatoes and toss them in a bowl with olive oil, salt, and pepper. Spread the sweet potato slices in a single layer on a baking sheet and roast for 15 minutes.

Roll out a chilled sheet of puff pastry onto parchment paper, forming a large circle roughly 12 inches in diameter.

Spread the caramelized onions evenly across the center of the rolled-out puff pastry, leaving a 2-inch border. Layer the roasted sweet potato slices on top and crumble the feta cheese over the vegetables.

Carefully fold the border of the pastry over the filling, creating pleats. Beat an egg and brush it over the exposed pastry edges.

Transfer the galette to a baking sheet and bake for 25–30 minutes, until the pastry is golden brown.

Remove the galette from the oven, allow it to cool for a few minutes, slice into wedges and serve warm.