In turn, poach the artichokes, mushroom and potatoes in the simmering liquid until they are cooked through. Cool in the refrigerator and slice into 1-inch thick pieces. Season the vegetables with extra virgin olive oil and salt.
To assemble the en papier, lay out a large square of parchment paper. Layer the ingredients by placing a couple slices of potato and mushroom on the parchments, followed by a couple of perch fillets, artichoke slices and Meyer lemons. Top with a pat of butter and 2 ounces of poaching liquid. Fold the edges of the parchment together and seal.
Bake the fish in the oven until just cooked through, approximately 10-15 minutes. Remove from the oven and let cool for a minute or two before opening, being careful to avoid the hot steam. Sprinkle olive oil, Meyer lemon zest and sea salt over before enjoying.