Combine spinach, jalapeño, shallot, anchovy, water, ¾ cup cilantro, 2 tablespoons lime juice and ¼ teaspoon salt in a blender; process until smooth, about 30 seconds. Transfer to a small bowl, cover and let stand at room temperature until ready to serve.
Toss cabbage, ¼ teaspoon salt and the remaining ¼ cup cilantro and 2 tablespoons lime juice together in a medium bowl.
Heat a grill pan over medium-high heat. Coat both sides of fish with oil and sprinkle with pepper and the remaining ¼ teaspoon salt. Cook, flipping once, until the fish is opaque and flakes easily with a fork, 3 to 5 minutes per side (depending on thickness).
Divide rice among 4 bowls and top each bowl with fish, avocado and cabbage slaw. Drizzle the bowls with salsa verde. Garnish with additional cilantro leaves and serve with lime wedges, if desired.
