In a medium bowl, add the parsley, cilantro, chives, garlic, lemon zest, 1 teaspoon salt, ½ teaspoon pepper, and the olive oil. Mix everything together and set aside.
Place a medium sauté pan over medium high heat and add the butter.
Season the thinly sliced heart with salt and pepper.
Once the butter is melted and foaming, add the heart and cook, stirring often for about 2-3 minutes, until the heart is cooked to medium and the butter is lightly browned.
Spoon the pieces of heart onto a serving plate as well as the browned butter.