Using a vegetable peeler, carefully shave each zucchini lengthwise into thin, delicate ribbons. Work your way around until you reach the seedy core.
Place zucchini ribbons in a colander set over a bowl. Sprinkle with 1 teaspoon salt and toss gently. Let rest for 10 minutes to draw out excess moisture.
While the zucchini rests, whisk together the olive oil, lemon juice, lemon zest, minced garlic, and a pinch of salt and pepper in a small bowl.
Gently squeeze the zucchini ribbons to remove excess moisture, then pat dry with a clean kitchen towel or paper towels.
Place the dried zucchini ribbons in a mixing bowl and pour the dressing over them. Add half of the fresh herbs and toss gently to coat evenly. Let marinate for 5 minutes.
Arrange the dressed zucchini ribbons on a serving platter. Tear the burrata into pieces and nestle them throughout the salad.
Drizzle with additional olive oil, sprinkle with the remaining fresh herbs, toasted pine nuts, and red pepper flakes if using. Finish with a final seasoning of sea salt and freshly ground black pepper to taste.