In a skillet, combine equal parts butter and olive oil over medium-low heat. Add thinly sliced onions along with a pinch of salt, stirring occasionally for about 20-25 minutes.

Preheat your oven to 200°C (400°F). Toss your sliced sweet potatoes in a bowl with olive oil, salt, and pepper until well coated. Spread them on a baking sheet and roast for about 15 minutes.

Roll out the chilled puff pastry on a lightly floured surface until about 1/8 inch thick. Transfer to a parchment-lined tray and leave a 2-inch border.

Arrange the roasted sweet potatoes over the caramelized onions, crumble feta cheese on top, and sprinkle fresh thyme.

Fold the edges of the pastry over the filling, pleating as needed. Brush with beaten egg.

Bake the galette for 25-30 minutes or until the pastry is puffed and golden brown.

Let the galette cool for a few minutes before slicing. Serve warm, optionally garnished with olive oil or fresh herbs.