Position a rack in the center of the oven and preheat to 400 degrees F. Line a baking sheet with parchment.
Whisk the cream, egg and milk powder together in a liquid measuring cup. Pulse 20 of the chives, 1/2 cup of the dill and 1/2 cup of the parsley in a food processor until finely chopped. Add the flour, baking powder and kosher salt and pulse until well combined with the herbs. Add the cheese and pulse a few times to combine.
Cut the cold stick of butter into pieces. Add to the food processor a few pieces at a time, pulsing until only a few pea-size pieces remain. Transfer to a large bowl and make a well in the center. Pour the wet ingredients into the well and mix with a fork, incorporating the dry ingredients a little at a time until a shaggy dough forms (it's okay if the dough looks a little dry, just don't overwork it). Lightly knead the dough in the bowl until it just comes together.
Turn the dough out onto a lightly floured surface and pat into a 3/4-inch-thick rectangle (about 9 by 7 inches). Use a floured 2-inch-wide heart-shape cookie cutter to stamp out 20 hearts as close together as possible (to minimize scraps). Arrange four of the hearts in a four-leaf clover pattern (with the points of all the hearts meeting in the center) on the prepared baking sheet. Repeat with the remaining hearts for a total of five clovers, spacing them evenly apart. Freeze for 15 minutes.
Brush the tops lightly with cream and sprinkle with sea salt. Bake the scones until golden brown, 23 to 25 minutes.
Meanwhile, pulse the remaining 10 chives, 1/4 cup dill and 1/4 cup parsley in a food processor until finely chopped. Add the stick of room-temperature butter and pulse until mixture is light green and well combined. Serve the scones warm with the herb butter.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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