Whisk lemon juice, oil, honey, mustard, garlic, salt and pepper together in a small bowl until emulsified. (Alternatively, place ingredients in a Mason jar or other container with a tight-fitting lid; shake until combined.)
Using a vegetable peeler or a mandoline, shave zucchini lengthwise into thin ribbons; discard seedy centers. Transfer to a large serving dish. Add 2 tablespoons of the dressing, basil and dill; toss until fully coated. Top with burrata and drizzle with the remaining dressing. Garnish with additional dill and pepper, if desired.
