In a large nonstick skillet, heat oil over medium-high. Sauté garlic for 1 minute. Season shrimp with 1/4 tsp salt and add to skillet. Cook, stirring occasionally, until shrimp are golden and cooked through, about 5 minutes. Transfer to a plate.
Add spinach to skillet and cook, tossing, until wilted, about 1 1/2 minutes. Transfer to plate with shrimp.
Add cream cheese and pesto to skillet and cook over low heat, stirring, until cream cheese is melted. Add zucchini noodles and remaining 3/4 tsp salt and cook, tossing, for 2 minutes. Add tomatoes. Cook just until zucchini noodles are almost wilted, about 1 minute.
Add shrimp, spinach, and lemon zest to skillet. Cook over medium heat, tossing, until shrimp and spinach are hot and zucchini noodles are wilted, about 1 minute. Spoon into bowls. Sprinkle with Parmesan.
Serving size: 1 1/2 cups noodles and shrimp and 2 tsp Parmesan.