In a medium saucepan set over medium heat, combine the shallots, lemon juice, and wine. Cook, stirring occasionally, until the shallots are tender and the liquid is almost completely reduced, about 4 minutes. Remove from the heat and let cool for 1 minute.
Stir in the cream to cool the mixture slightly.
Place the saucepan over medium-low heat and whisk continuously. Add the butter, one piece at a time, allowing each piece to fully incorporate before adding the next, until the sauce is thick, glossy, and emulsified. If the sauce begins to simmer, remove the pan from the heat and whisk in another piece of butter to bring the temperature down.
Remove from the heat. Add the salt, white pepper, chives, and lemon zest. Taste and add more salt, if needed. Cover and keep warm until ready to serve.
Season the salmon generously on both sides with salt and pepper. Sprinkle the cassava flour over the fillets and rub to coat both sides evenly. Shake off any excess.
Heat the oil in a large nonstick skillet over medium-high heat until shimmering. Add the salmon and sear until golden brown, about 3 minutes per side for medium.
Divide the salmon among four shallow bowls or plates. Spoon 1 to 2 tablespoons of the lemon-chive beurre blanc over each fillet. Garnish with more fresh chives. Serve immediately.