Place herbs, garlic and pepper in a food processor or blender, and pulse to combine, stopping to scrape down the sides of the container if necessary.
Add yogurt and purée until smooth. (This may take a minute or so; scrape down the sides of the container as needed.) With the motor running, gradually drizzle in the olive oil. Pulse in lemon zest and salt. Taste and add more salt if needed.
Use immediately or refrigerate in an airtight container for up to 5 days. Spoon over grilled or roasted chicken, seafood (especially shrimp and salmon), sausages, steaks, lamb chops and vegetables. Use as a marinade for chicken, lamb or pork; as a dressing for starchy salads with beans, potatoes or grains, or for hearty vegetable salads, like those with cucumbers or blanched and sliced sugar snap peas or green beans. Serve as a dip for crudité or chips. Spread in roast beef, lamb or pork sandwiches.