Cook linguine to al dente, according to the instructions on the package.
Meanwhile, heat olive oil in a large skillet over medium heat. Add onion and garlic and sauté until onions have started to turn translucent, about 4 minutes. Next, add spinach and cook for another 3 minutes. Add zucchini and sauté until zucchini is crisp tender, about 2 minutes.
Drain the clams, reserving 1/2 cup of the clam juice. Add the clams, bouillon, basil, pepper, and reserved clam juice to the skillet. Bring to a boil. Simmer until vegetables are tender, about 5 minutes.
Divide pasta evenly among 6 plates. Divide clam sauce evenly over the 6 prepared plates. Top with shredded Parmesan cheese. Serve hot.