Brush the zucchinis with 2 teaspoons of oil and place on the grill cut side down. Grill until nicely charred and softened. Remove and transfer to a large plate.
In a small pan, heat the remaining olive oil with capers, anchovy, garlic, and lemon zest. When just starting to simmer, remove from heat and let cool. Stir in parsley.
Drizzle the zucchini with the caper sauce and serve immediately.