Peel and Slice the Onions — Peel the onions and slice them thinly into even rings or half-moons.

Heat the Pan — Heat the olive oil and butter in a large skillet over medium heat until melted.

Start Cooking the Onions — Add the sliced onions and a pinch of salt. Cook over medium heat for 8–10 minutes, stirring occasionally, until softened.

Add Sugar and Reduce Heat — Sprinkle the sugar over the onions and reduce the heat to medium-low.

Caramelize Slowly — Continue cooking for 15–20 more minutes, stirring every 5 minutes. Add a splash of water or broth if the onions begin to stick.

Finish with Balsamic — Stir in the balsamic vinegar during the last 2–3 minutes of cooking, then cook until glossy and deep golden. Remove from heat and let cool slightly.

Prepare the Muffin Tin — Lightly drizzle olive oil into each cup of a 12-cup muffin tin. Use a paper towel to spread it evenly.

Cut the Puff Pastry — Roll out the thawed puff pastry sheets. Cut the first sheet into 9 equal squares, then cut 3 squares from the second sheet for 12 total. Press each square into a muffin cup to form a pastry shell.

Pierce the Base — Use a fork to prick the bottoms of the pastry cups (not the sides) to prevent puffing.

Add the Fillings — Spoon caramelized onions into each cup, top with a piece of brie, then add 1 teaspoon of fig jam. Finish with a piece of prosciutto and a few rosemary leaves.

Bake Until Golden — Bake at 350°F on convection for 25–30 minutes, or until the pastry is golden and crisp.

Serve Warm — Remove from the muffin tin and serve warm.