Rinse the zucchini and pat them dry. Trim off the ends. Cut each zucchini in half horizontally, then cut each of those pieces in half lengthwise.
Cut each plank in half again lengthwise. Now slice the planks horizontally into triangles about ⅓-inch thick.
Peel and press the garlic. Heat the oil in a 6-quart pot on medium-high. Add the garlic and cook, stirring, for one minute.
Add the zucchini wedges, tomato paste (or tomatoes), salt & black pepper to the pot and stir to mix. Cover the pot, put the heat on medium-low and cook the zucchini until it's just tender (about 12 minutes). Stir periodically to prevent sticking.
Remove the lid and add the chicken stock and hot water. Stir to blend. Increase the heat to high, cover, and bring the liquid to a boil.
When the pot is boiling, add the pasta and stir periodically to prevent sticking. Cook the pasta until it's al dente.
When pasta is cooked, do NOT drain it. Turn off the heat and stir in Parmesan cheese. Add red pepper flakes.
Ladle it into bowls and serve with additional grated Parmesan.
Immediately store any leftover broth in a separate container so it does not make the leftover pasta soggy. Store the leftovers separately in the refrigerator for up to four days. Reheat the pasta in the microwave with some broth added.
Video
Notes
If you want to make half a pound of pasta instead of a pound, you can either halve the entire recipe or just make half a pound of pasta and keep all other ingredient amounts the same. You'll have extra broth to use when serving and to save for leftovers.
If you're serving this as a vegetarian meal, use vegetable stock. Note that some vegetarians don't eat Parmesan cheese, because it contains an animal enzyme. You might need to omit it.
For a vegan version, use vegetable stock instead of chicken stock and omit the Parmesan. You could try adding vegan Parmesan instead.