Rinse whole zucchini and pat dry. Trim off 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 just over ¼-inch thick.
Heat oil in a 6-quart pot on medium high. Add pressed garlic and cook, stirring, for one minute.
Add zucchini, 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 zucchini until just tender (about 12 minutes), stirring periodically to prevent sticking.
Remove the lid and add chicken stock and hot water. Stir to blend. Increase heat to high, cover, and bring liquid to a boil.
When the pot is boiling, add pasta and stir periodically to prevent sticking. Cook pasta until al dente (taste it when there are three minutes left on the al dente time recommended on the package.)
When pasta is cooked, do NOT drain. Turn off the heat and stir in Parmesan cheese. Add red pepper flakes.
Ladle 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.
If you have leftover tomato paste from this recipe, you can wrap 1-2 tablespoons of paste at a time in plastic wrap. Then place those packets in a freezer bag. I do this all the time and add the tomato paste to soups and stews.