In 12-inch nonstick skillet, heat oil over medium-high heat.
Add zucchini and salt; cook 4 to 6 minutes, stirring occasionally, until crisp-tender. Remove with slotted spoon; reserve.
Heat same skillet over medium heat; add garlic and pasta.
Cook 2 to 3 minutes, stirring frequently, until garlic is fragrant and pasta is lightly toasted.
Add broth; cover and simmer 10 to 11 minutes or until liquid is nearly absorbed.
Stir in shrimp, butter and zucchini; cover and cook 3 to 4 minutes or until shrimp are pink and pasta is tender.
Stir in cheese, lemon, and thyme; garnish with parsley.