Pat the halibut fillets completely dry with paper towels. Season generously with kosher salt and black pepper.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat until shimmering.
Place the halibut fillets in the pan and sear without moving for 4 minutes until a golden crust forms.
Flip the fillets carefully and cook for another 2 to 3 minutes until the fish is opaque and easily flakes.
Remove the fish from the pan and set aside. In the same skillet, add the spinach and saute for 1 minute until wilted, then remove to serving plates.
Lower the heat to medium-low. Pour in the white wine and lemon juice, scraping up browned bits. Simmer until reduced by half.
Stir in the heavy cream. Turn heat to low and whisk in the remaining 3 tablespoons of cold butter, one piece at a time, until the sauce is smooth and emulsified.
Serve the seared halibut over the wilted spinach, drizzle generously with the lemon beurre blanc, and garnish with fresh chives.