Preheat the broiler and position a rack 8 inches from the heat. Bring a large saucepan of water to a boil. Add the chives and spinach and blanch for 30 seconds, just until bright green. Drain and rinse under cold water; squeeze dry. Transfer the chives and spinach to a blender. Add the extra-virgin olive oil and puree until smooth. Season with salt.
Rinse out the saucepan and fill it with cold water. Add the potatoes and bring to a boil. Simmer until the potatoes are tender, about 10 minutes. Drain the potatoes and cut them into thin coins.
In a microwave-safe bowl, combine the olives with the pure olive oil. Microwave at high power in 2-minute bursts until the olives are golden and crisp, 5 to 6 minutes depending on the microwave. Drain the olives and transfer to a paper towel–lined plate to cool. Reserve the oil for another use.
Place the cod on a foil-lined baking sheet, brush with the mustard and season with salt and pepper. Broil for about 10 minutes, until the fish is cooked through and lightly browned on top; transfer to plates and spoon the potatoes alongside. Sprinkle with the olives, drizzle the chive puree all around and serve.
