Preheat oven to 375°. Start beurre blanc: In a small saucepan, combine shallot, herbs, white wine, and vinegar. Bring to a boil over medium-high heat, uncovered, and cook until liquid has reduced by half, about 4 minutes. Stir in cream, salt, and pepper and remove from heat.
Drape a long piece of kitchen twine crosswise across an 8- by 13-in. glass baking dish, long enough so ends of twine extend several inches beyond dish on either side. Set a large piece of parchment (about twice the width of pan) over twine.
Season fish on both sides with salt and pepper, then lay in pan, bottom (skinned) side down. Arrange lemon slices, butter, and herbs on top of fish and drizzle with oil and wine. Fold ends of parchment paper over fish and tie closed with kitchen twine. Set pan in oven and steam 10 minutes.
While fish is steaming, finish beurre blanc: Bring sauce to a simmer over medium-low heat. Slowly whisk in butter, a few pieces at a time and melting each batch before adding the next, until sauce is smooth and velvety, about 5 minutes. Strain sauce through a fine-mesh strainer and season to taste with salt. Keep hot if needed by immersing bottom of pot in a large bowl of hot water.
Lift parchment package carefully to a deep platter. At the table, snip twine and open package. Serve fish drizzled with beurre blanc.
*Try to get evenly thick fillets so they'll cook at the same rate. If the fillets are closer to 1 in. thick, increase cooking time to 12 minutes. To remove pin bones, which run lengthwise along fillet, grasp with tweezers and pull out in the same direction that bones are pointed.