For the dough: In a medium bowl, mix together the flour and butter with your fingers until the butter is just mixed in throughout the flour. Add the chilled water 1 tablespoon at a time and mix it into the flour mixture with your fingers. Use just enough water so that the dough just comes together. Gather the dough into a ball and wrap in parchment paper. Set it aside in the refrigerator or until ready to use.
For the filling: Cut the acorn squash into thin slices. In a medium skillet over medium heat, add 2 tablespoons butter and 2 tablespoons olive oil. Add the sliced squash and 1/4 cup water, cook until the squash is soft and cooked through, about 10 minutes. Sprinkle with the salt and pepper. Add the heavy cream to the pan halfway through, about 5 minutes into the process.
Remove the squash from the pan and set aside in a bowl to cool. Once the squash has cooled, toss together with the cheese.
Melt 1 tablespoon butter and 1 tablespoon olive oil in the pan. Add the sliced onion and sugar and cook over low heat about 30 minutes, until the onion has browned and caramelized. After the onion has cooked, divide the mixture into 6 equal portions and let cool.
Preheat the oven to 375 degrees F.
Remove the dough from the refrigerator and allow it to come to room temperature for about 10 minutes. Cut the dough into 6 equal portions. Take each portion and roll it out into a small circle, about 3 inches in diameter. The dough does not have to be rolled out perfectly evenly¿a galette is a rustic, free-form tart.
In the center of each galette, place a portion of the cooled caramelized onion and squash mixture. Create an edge to the galette by folding the edges of the pastry up towards the center and pressing down gently. Don't cover the filling with the pastry.
Place the pastries onto a baking sheet lined with parchment paper. Bake for 25 minutes until the crust is lightly browned. Drizzle a little extra virgin olive oil and kosher salt over each galette.
Serve slightly warm with mixed greens.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.