In a medium saute pan over medium heat, add olive oil and butter. When butter begins to foam, add onions and sweat 2 minutes. Add zucchini and garlic and cook 2 to 3 minutes. Add tomatoes, tomato paste, salt, and pepper, and cook 5 minutes. Remove from heat and let cool to room temperature. Once cooled, mix in 3 tablespoons bread crumbs, cheese, balsamic vinegar, anchovy paste (if desired), and basil. Gently spoon mixture into each zucchini flower.

In a small, shallow bowl, whisk together egg and cream. Place 3 cups bread crumbs in a second shallow bowl. Dip each stuffed flower into the egg-cream mixture, allowing excess to drip back into the bowl, then roll in bread crumbs, coating well. In a medium frying pan over medium-high heat, add vegetable oil. Pan-fry flowers on all sides until lightly browned. Remove to paper towels to absorb excess oil. Serve immediately. Yield: 12 pieces