Heat the oven to 400˚F. Brown the 4 tbsp of butter in a small saucepan. Meanwhile, cut a piece of parchment paper roughly 16 inches by 24 inches for each fish fillet. Fold the parchment paper in half to create a seam, then open it back up. Place the fish along the seam skin side down and season with kosher salt. Add asparagus tips, olives, capers, and parsley. Spoon the brown butter over everything. Butter the perimeter of the parchment paper, then fold it back in half, pressing to seal the sides. Working from top to bottom, fold the parchment paper in on itself toward the fish (like this). Transfer to a parchment paper-lined sheet pan. Cook for 10 minutes per inch of thickness.
To serve, plate the packet and slice to vent the steam.