2 Tbs. olive oil, divided
2 cups finely julienned red onions
4 sprigs thyme, leaves picked and chopped, sprigs reserved
1 clove garlic, finely chopped
2 Tbs. red wine
2 Tbs. balsamic vinegar
2 Tbs. light brown sugar
1 large butternut squash, about 1½ lbs., peeled and cut to split the smaller top from the large bottom
1 cup diced yellow onion
2 cups vegetable stock
4 Tbs. unsalted butter, melted
1 sheet store-bought puff pastry, Dufour recommended
1 egg, beaten
1⁄2 cup shaved hard goat cheese, such as drunken goat or Garrotxa, available at the Whole Foods cheese counter
Flaked sea salt, Bulls Bay Saltworks salt flakes recommended
2 tsp. thyme leaves, for garnish
For the red onion jam:
Heat one tablespoon of the olive oil until shimmering in a heavy-bottomed saucepan over medium heat. Add the onions. Cook, stirring frequently, for about five minutes, until soft and just starting to color. Add the chopped thyme leaves and garlic and cook for about one minute, until fragrant. Add the red wine and cook for about two minutes to let the alcohol evaporate and the wine reduce slightly. Add the balsamic vinegar and brown sugar, reduce the heat to low, and simmer, stirring occasionally, for 10 minutes, until thick. Remove from the heat and allow to cool.
For the squash purée:
Dice the bottom piece of the butternut squash into one-inch pieces. Heat the remaining tablespoon of olive oil in a medium saucepan over medium-high heat. Add the diced yellow onion and cook until soft, two to three minutes. Add the diced squash and the vegetable stock. Reduce the heat to medium and simmer, stirring occasionally, for 10 minutes, or until the squash is tender.
Strain, discarding the liquid. Place the solids in a food processor, drizzle in two tablespoons of the melted butter, and purée.
Allow to cool.
Preheat the oven to 350°F.
Split the remaining top of the butternut squash down the middle and cut the halves into semicircular slices, about 1⁄8 inch thick.
Place the puff pastry sheet on a parchment paper-lined baking sheet. Evenly spread the cooled onion jam onto the pastry, leaving around 1⁄4 inch on each side for the crust. (There may be a little jam left over.) Evenly spread the squash purée on top of the jam. (There may be a little purée left over.) Place the squash slices in slightly overlapping rows on top of the squash purée, then brush them with the remaining two tablespoons of melted butter. Brush the edges of the pastry with the beaten egg. Bake for 15 to 20 minutes, until the edges are puffed and golden and the squash is tender. Top with a few shavings of goat cheese and a pinch of sea salt, and a sprinkle of thyme leaves and serve immediately.