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1
Cook the barley according to package directions until very tender.
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2
Drain and chill in the refrigerator at least 3 hours.
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3
Put the chilled barley in a food processor and process until smooth.
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4
Add the egg yolk, Monterey Jack, 1/4 cup of the Parmesan, and 1/3 cup of the flour; process just until mixed.
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5
Transfer the mixture to a bowl and stir in the grape leaves, salt, and pepper.
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6
Beat the egg whites until stiff, but not dry.
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7
Gently fold into the barley mixture along with another 1/3 cup of flour.
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8
Line a baking sheet with waxed paper.
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9
Place the remaining flour in a shallow dish.
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10
Using 2 spoons, shape about 2 heaping tablespoons of the barley dough into a small football shape, drop it into the flour, and coat it lightly.
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11
Transfer to the lined baking sheet and repeat the process until all the dough has been used.
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12
Bring a large pot of salted water to a boil.
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13
Drop 6 to 8 dumplings at a time into the water and cook until they float to the top, about 1 minute.
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14
Remove the dumplings from the pot with a slotted spoon and drain on paper towels.
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15
When all the dumplings have been cooked, arrange them in a single layer in an ovenproof baking dish.
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16
Drizzle with the melted butter and sprinkle with the remaining Parmesan cheese.
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17
(The dumplings may be prepared up to this point and refrigerated 1 to 2 days before baking.)
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18
Preheat the oven to 375F.
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19
Bake the dumplings until they are puffed and light golden brown, 25 to 30 minutes.
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20
Sprinkle with the parsley and serve at once.
