01 - Combine cranberries, sugar, water, orange zest, and salt in a small saucepan. Simmer over medium heat, stirring occasionally, until cranberries burst and sauce thickens, about 8 to 10 minutes. Set aside to cool slightly.
02 - In a bowl, mix ground turkey, onion, garlic, parsley, Dijon mustard, salt, and pepper until just combined. Shape into 4 equal patties.
03 - Heat olive oil in a large skillet over medium heat. Cook patties 5 to 6 minutes per side until golden brown and internal temperature reaches 165°F. Transfer to a plate.
04 - Melt butter in a skillet over medium heat if using, then toast buns cut side down until golden.
05 - Place lettuce on bottom bun halves, layer with turkey patty, Brie slices, cranberry sauce, and red onion if using. Cover with top bun.
06 - Serve immediately while warm and melty.