Heat 2 tablespoons of the olive oil in a dutch oven or large pot over medium heat. Add the carrots, celery, 4 of the sliced garlic cloves and season with 1 teaspoon salt and as much pepper as you like. Stir regularly to combine and cook the carrots and celery until softened, about 7 minutes.
Add the pasta to the pot, followed by the clam juice and chicken broth. Bring to a simmer, stirring often and cook the pasta until al dente then stir in the peas and white parts of the scallion and turn off the heat. Season with salt, as needed and set aside until ready to serve.
While the pasta is cooking, add ginger, almonds, lemon zest and juice, spinach, butter, add the remaining 3 tablespoons of olive oil and remaining 2 sliced garlic cloves to a food processor. Pulse until the mixture is fully blended and the spinach becomes one with everything. Season with salt and pepper and transfer to a serving bowl.
When ready to serve, heat the soup back up to a simmer and add the cod pieces and keep simmering until cooked through and starting to flake apart, about 5 to 7 minutes. Season the soup with salt, if needed then ladle into bowls and stir in a generous amount of pesto and the green parts of the scallion into each bowl.