To make the caramelized onions, thinly slice the onion. Melt the butter in a skillet over medium heat. Cook the onions for about 15 minutes, until golden brown and sweet, stirring occasionally.
In a bowl, combine the ground beef with the minced garlic, salt, pepper, and chopped fresh thyme. Form the mixture into two equal-sized patties.
Heat a skillet or grill to medium-high heat. Cook the patties for about 3-4 minutes per side, or until nicely browned and cooked through.
During the last minute of cooking, place a slice of Camembert cheese on top of each patty to allow it to melt slightly.
Halve the hamburger buns and toast the cut sides in a dry skillet for about 1 minute, until lightly golden.
Spread Dijon mustard and mayonnaise on the bottom bun, then top with arugula.
Place the patty with the melted Camembert cheese on top of the arugula, then pile on the caramelized onions.
Top with the other half of the bun and serve immediately while the cheese is still melted.
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