Preheat oven to 400 degrees F.

Dry the barramundi fillets with a paper towel and sprinkle each piece generously with salt and pepper. Set aside. Zest the entire lemon and then cut half of the lemon into 4-5 thin slices. Juice the remaining half of the lemon into a small bowl and set aside.

Lay two large pieces of parchment paper (about 12" x 12") side by side. Divide the sliced shallots and baby spinach between each piece of parchment, and sprinkle the spinach and shallots with a pinch of salt and pepper. Lay the barramundi fillets on top of the spinach and shallots, and top each fillet with the thin lemon slices. Drizzle about 1 Tablespoon of olive oil over the fillets. One sheet at a time, close the parchment paper packets: bring two opposite sides of the paper together and fold them together several times to create a tight seal. Then fold up each end of the paper to create a tight seal on all sides. It's fine if the seals loosen slightly in this process.

Place the parchment paper packets on a large baking sheet and bake the barramundi on the middle rack of the oven for 10-12 minutes, or until the fish is tender and flakes easily.

While the fish is cooking, bring a small skillet to medium heat. Add the remaining tablespoon of olive oil to the pan, and once hot add the chopped almonds. Sauté for 2 minutes, then add the dates and cook until warmed through, stirring regularly, about an additional 2 minutes. Turn off the heat and stir in the lemon zest, lemon juice, and parsley. Season with a pinch of salt and pepper, or to taste.

Open the barramundi packets and transfer the fish, spinach, shallots, and lemon slices to two plates. Top each piece of barramundi with the date-almond mixture and serve immediately.