In a bowl, combine parsley, mint, garlic, and 1 tablespoon olive oil. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Rub artichoke hearts inside and out with herb mixture. Place them stem-side up in a medium pot. Add remaining 1/4 cup olive oil and enough water to come halfway up the sides of the artichoke hearts.
Place pot on the stove over high heat and bring to a boil. Reduce heat to low, cover pot, and simmer until artichokes are tender, about 20 minutes. Remove from heat and add remaining herbs. Cool completely in the cooking liquid.
Divide artichoke hearts onto four plates, and serve at room temperature with some of the liquid spooned over the top.