Whip butter in a food processor until smooth and light. Combine strawberries, sauce, and jam in a small bowl. Once combined, add to butter and pulse until well combined. Set aside. Combine chives and cilantro in a small bowl. Spread half of the mixture over a piece of parchment paper. Place butter over herb mixture and top with remaining herbs. Roll into a log shape, using edge of baking sheet to form a tight log. Chill for 2 hours before serving.