Prepare the rosemary aioli by whisking together mayonnaise, Dijon mustard, rosemary, garlic, and lemon juice in a small bowl. Chill until ready to use.
Melt butter in a skillet over medium heat. Add pear slices and cook for 2-3 minutes per side until golden. Drizzle with honey and balsamic glaze, then remove from heat.
In a mixing bowl, combine ground beef, salt, pepper, and smoked paprika. Form into four patties.
Heat a grill or skillet over medium-high heat. Cook patties for 3-4 minutes per side. Add Brie slices during the last minute to melt.
Spread rosemary aioli on the bottom halves of toasted brioche buns. Add arugula, Brie-topped patties, caramelized pears, and pancetta (if using). Top with the bun tops and serve immediately.
Notes
To enhance flavor, try grilling the brioche buns lightly. Substitute pancetta with crispy bacon for a different twist.