• Melt the butter with the olive oil in a large skillet over medium heat. Add the sliced onions and a pinch of salt.
• Cook for about 20-25 minutes, stirring occasionally, until the onions are very soft, deep golden and caramelized.
• Reserve ½ cup of the caramelized onions for the dipping sauce.
• Push the remaining onions to the edges of the skillet and add the ground beef. Cook, breaking it into small crumbles, until deeply browned.
• Add the garlic, Worcestershire, Dijon, thyme, salt and pepper.
• Pour in the beef broth and scrape up all those browned bits from the bottom. Cook for another 2-3 minutes until the liquid has mostly evaporated.
• Heat the oven to 425°F and lightly grease an 18×13-inch rimmed half-sheet pan.
• Lay 6 tortillas around the perimeter of the pan, overlapping them so approximately half of each tortilla hangs over the edge. Make sure the tortillas also overlap each other enough that there aren't gaps in the bottom.
• Place 1 tortilla in the center to completely cover the bottom.
• Sprinkle about half the cheese mixture over the tortillas.
• Spread the French onion beef mixture evenly over the cheese, then follow with the remaining cheese.
• Place the last tortilla in the center on top. Fold all of the overhanging tortillas inward over the filling, overlapping them to completely enclose the quesadilla.
• Brush the top lightly with melted butter.
• Bake for 18-20 minutes.
• Carefully remove the top sheet pan and bake uncovered for another 5-8 minutes, until the tortillas are deeply golden and crisp.
• Let them rest about 5 minutes before cutting.
• While the quesadilla bakes, finely chop the reserved caramelized onions.

Combine all of the French onion dip ingredients.

• Taste the dip, then adapt as necessary. It should be tangy and savory, because it's going against a very rich, cheesy quesadilla.
• Refrigerate the dip until ready to serve.
• Cut the entire sheet-pan quesadilla into 16 squares or rectangles with a large pizza cutter.
• Pile them onto a big serving board or platter with the Greek yogurt French onion dip right in the middle.
• Finish the quesadillas with fresh thyme or finely chopped chives. Around the dip, you could add a few simple crunchy things, such as pickles and kettle chips.