Place the oven rack on the top setting. Preheat broiler to high. Line a baking sheet with foil. Pat the salmon fillet dry and place it onto the baking sheet. Season is generously with salt and pepper.
In a small bowl, stir together the birch syrup and mustard until smooth. Spoon half of the mixture evenly over the top of the salmon fillet, spreading to coat. Broil the salmon until it begins to brown on top, about 6-7 minutes for medium, watching closely. Rotate pan as needed to cook evenly. Cooking time will vary depending on the thickness of your fillet, so keep an eye on it and adjust cooking time as needed.
Top the salmon with lemon slices and parsley (if using). Portion by pulling the salmon away from the skin with a fork. Drizzle with remaining birch syrup glaze. Serve promptly while hot.