In a skillet, saute spinach in 1/2 tablespoon butter for 1 minute, stirring constantly. In a small bowl, stir flour, 2-3 tablespoons milk and salt until smooth. Add to spinach; cook and stir until thickened, about 1 minute. Set aside and keep warm.
In another bowl, whisk eggs, salt, pepper and remaining milk. In another skillet over medium heat, cook egg mixture in remaining butter. As the eggs set, lift edges, letting uncooked portion flow underneath. When eggs are set, spread spinach mixture over half of the omelet. Fold omelet in half and transfer to a warm platter.