Heat a large cast iron skillet or large dutch oven over medium heat and drizzle in the oil and the butter. Once hot, add the onions. Stir and cook for five minutes and then reduce the heat to low. Add a pinch of salt and continue cooking for 45 minutes to 1 hour, until deeply caramelized, stirring occasionally. Remove from the heat and let cool completely, ideally overnight.

Meanwhile, heat the oven to 400ºF. Drizzle the garlic with a little bit of olive oil. Wrap in aluminum foil (or use parchment) and bake for 40 to 45 minutes, until softened. Let cool and then pop the cloves out of their paper and set aside.

Line a baking sheet with parchment paper. Lightly flour a work surface area. Roll the puff pastry into a large rectangle (about 10 by 16-inches) and transfer to the baking sheet. Use a knife to run a 1-inch border around the edges, being careful not to pierce all the way through. Use a fork to poke holes throughout the center of the tart all over.

Heat the oven to 375ºF. Scatter the cheese all over the tart. Add the roasted garlic to the tart and then top with the onions and thyme. Brush the edges of the tart with milk or use an egg wash.

Bake for 20 minutes. Increase the temperature to 400ºF and bake for six to eight minutes, until the edges are browned, puffy and crispy. Let the tart cool slightly before slicing. Serve and enjoy!