Cook and stir onion, 1 tablespoon vegetable oil, and 1 teaspoon salt in a saucepan over medium heat until onion is translucent, 5 to 10 minutes. Stir in green curry paste; cook and stir until fragrant, 2 to 3 minutes.

Pour chicken broth into curry-onion mixture; bring to a boil and add peas. Cover the pot with a lid and cook until peas are just tender, about 2 minutes.

Pour peas mixture into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth. Pour pureed pea mixture through a fine-mesh strainer into the same saucepan; set over low heat. Stir in fish sauce and lime juice; season with green curry paste and salt to taste.

Season black cod pieces all over with salt.

Heat 1 teaspoon vegetable oil in a nonstick skillet over medium-high heat. Place cod, skin-side down, in hot oil and cook, turning once, until fish flakes easily with a fork, 4 to 6 minutes.

Ladle green curry sauce into 4 bowls. Place 2 pieces of cod, skin-side up, in sauce and garnish with strawberries and mint.