Cut the stems off the jalapeños. Taste for spice level and remove seeds if desired for a milder sauce. Roughly chop the jalapeños and add them to a food processor along with the garlic. Pulse until coarsely chopped.

Add the cilantro, parsley, cumin, cardamom, and coriander to the food processor. Pulse until coarsely chopped, scraping the sides as needed.

Pour in the olive oil, lemon juice, sugar, and salt. Pulse until combined, ensuring the mixture remains chunky.

If the mixture is too stiff, add water one tablespoon at a time (up to 3 tablespoons) until the desired consistency is reached.

Taste the zhoug and adjust the salt, sugar, or lemon juice according to your preference.

Transfer the zhoug to a container and drizzle with olive oil. Let it rest for 1 hour at room temperature or refrigerate before serving.