Preheat oven to 350°F.
Score zucchini (like you’re dicing an avocado) and scoop out insides with a small spoon, leaving a ¼”-thick border intact. Chop zucchini pulp and set aside.
Place zucchini boats in a large baking dish and drizzle all over with oil.
Season the zucchini boats with salt and pepper and sprinkle thyme on top. Bake until tender, about 20 minutes.
In a large skillet over medium heat, melt butter.
Add shrimp and season with salt and pepper. Cook until pink and cooked through, 3 to 4 minutes.
Remove from heat, let cool, then chop into bite-size pieces.
Return the skillet to medium heat and melt the remaining 1 tablespoon of butter.
Add reserved zucchini pulp, tomatoes, and garlic, season with salt and pepper, and cook until fragrant, 1 minute more.
Add cream, Parmesan, and lemon juice, and cook until slightly reduced, 3 minutes. Remove from heat and fold in cooked shrimp.
Fill zucchini boats with shrimp mixture and top with mozzarella. Bake until cheese is bubbly, about 10 minutes more.
Garnish with more Parmesan and parsley, if desired, before serving.