Combine the garlic, parsley, lemon zest and juice, salt, butter, and olive oil in a bowl or food processor and mix together thoroughly. Place in the refrigerator until needed.
Preheat the oven to 350F.
Cut potatoes into half inch rounds. To blanch potatoes, place in a medium sized pot of water and bring to a boil. Remove from heat and strain when potatoes are cooked halfway through (5-8 minutes). Place potatoes in an ice bath to halt the cooking process.
Season the fish with the salt and pepper. Set aside in the refrigerator.
To assemble the pouches, divide beans and potatoes between 6 large, square pieces of parchment paper. Top with 1 cup of greens and one 4-ounce filet of fish.
Sprinkle the contents of each pouch with 1 tablespoon of wine.
Place 1 1/2 teaspoons of compound butter on top of each fish filet.
Fold the parchment paper around the edges tightly in 1/4 inch folds to create a half moon shape. Make sure that all edges are tightly sealed to avoid steam escaping.
Arrange the packaged fish on a sheet tray and place in the oven. Cook until the fish is fully cooked through (white and flaky), about 12-15 minutes.
Remove the sheet pan once finished and serve by carefully opening each parchment package and transferring contents to a plate.