Cut zucchini into noodles using a spiralizer (fitted with the large shredding blade). Let sit in a colander.
Heat olive oil in a large skillet over medium heat. Add onion and garlic; cook and stir until onion is translucent, about 5 minutes. Add chicken broth, lemon zest, 1/2 the lemon juice, and chile-garlic sauce. Add the zucchini noodles; season with salt and pepper and toss to coat. Cook until tender, about 2 minutes. Add shrimp; cook and toss until warmed through, about 2 minutes more. Top with Parmesan cheese.
