Wash and slice zucchini into half moons, with a thickness of slightly less than ¼ inch.
Peel and then thinly slice the garlic cloves.
In a large skillet over medium heat, sautee the garlic in the olive oil until golden, about 1-2 minutes.
Add all of the sliced zucchini, tossing to coat with the olive oil and garlic. Cook the zucchini/garlic mixture for about 15 minutes, stirring very infrequently. The goal is to brown the zucchini, with some pieces becoming almost charred. The garlic will become toasty -- don't fret, this is normal!
In the meantime, bring a large pot of salted water to a boil.
When the zucchini is done, remove from heat and season with salt, pepper and red pepper flakes to taste.
Cook the pasta one minute less than indicated on the box. Two minutes before the pasta is to be ready (i.e., 3 minutes less than the cooking time shown on the pasta box) warm the zucchini garlic mixture over medium-low heat.
When the zucchini is sizzling, add about ½ cup of pasta water to loosen up the zucchini and any bits stuck to the skillet.
When the pasta is done, use a mesh scoop or slotted spoon to transfer it to the skillet with the zucchini. Slowly stir the pasta into the zucchini. While continuing to stir, first add the lemon juice and then the grated cheese. If the the mixture seems too dry, add a bit more pasta water to loosen it up.
Scoop into bowls, toss with a bit more grated cheese, and serve immediately.