Preheat oven to 350°F. Coat 15x10x2-inch oval baking dish with 1 tablespoon oil.
Heat 5 tablespoons oil in heavy large skillet over medium-high heat.
Add onion and sauté until translucent, about 5 minutes.
Add breadcrumbs and thyme and stir until breadcrumbs are lightly toasted, about 3 minutes.
Transfer to large bowl.
Mix in tomatoes, cheese, eggs, garlic, salt and pepper.
Fill zucchini blossoms with breadcrumb mixture, using about 2 teaspoons for small blossoms and 1 tablespoon for large blossoms (be careful not to tear blossoms).
Sprinkle any remaining breadcrumb mixture over baking dish.
Place zucchini atop breadcrumbs in dish.
Drizzle remaining 2 tablespoons oil over. (Can be made 8 hours ahead. Cover; chill.)