Melt butter and olive oil in a large skillet over low heat.

Add onions, rosemary, and sugar to the skillet.

Cook, tossing occasionally, for 30-40 minutes, until onions are limp and golden brown.

Stir in sherry vinegar, scraping any browned bits from the bottom of the pan.

In a small bowl, whisk together milk and egg until smooth.

Stir the caramelized onions into the milk and egg mixture.

Preheat oven to 400 degrees Fahrenheit.

Line an 11x17 inch baking sheet with parchment paper.

On a lightly floured surface, roll out the puff pastry to a 9x12 inch rectangle.

Transfer the pastry to the prepared baking sheet.

Use a fork to spread the onion mixture evenly over the pastry, leaving a 1-inch border (let excess egg mixture drip back into bowl).

Arrange figs, cut-side up, in even rows on top of the onion mixture.

Scatter crumbled Stilton cheese and pine nuts over the figs.

Use a pastry brush to dab the edges of the tart with the egg mixture.

Gently fold over the edges of the tart to form a lip and brush with more egg mixture.

Bake in the preheated oven for 25-30 minutes, until the pastry is puffed and golden brown.

Serve warm or at room temperature, sprinkled with fresh rosemary needles and drizzled with honey, if desired.