For the brussels sprouts, melt 2 tablespoons of the butter over high heat in a large sauté pan. Add the onion and garlic and cook for 1 minute. Add the brussels sprouts and toss to combine. Continue to cook over high heat until the sprouts begin to brown, about 5 minutes. Add the water and season generously with salt. Cover the pan and reduce the heat to medium.
Gently sear the mahi mahi fillets, skin side down, in a small, dry ovenproof sauté pan over medium heat until they just begin to color, about 5 minutes. Transfer the pan to the oven and bake until the fish is an even color throughout, about 8 minutes.
For the flavored butter, mix the feta cheese with the remaining 4 tbsp butter and the parsley. Mash with a fork to combine, breaking up the feta as much as possible.
When the mahi mahi is done, uncover the sprouts and turn the heat up to high. When the liquid remaining in the pan has reduced enough to just barely coat the sprouts, remove from the heat and toss.
Arrange the fillets and brussels sprouts on a platter and put a dollop of the feta butter on each of the mahi mahi fillets. Serve family style.