Mama Mirabella's Ham and Cheese Ravioli

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1 pound sliced cooked ham, chopped

1 pound domestic Swiss cheese, sliced and chopped

3 cloves garlic, minced

1/4 cup chopped flat-leaf parsley

1 teaspoon salt, plus more for cooking water

1 teaspoon black pepper

2 eggs, beaten

1/2 cup Parmesan cheese

1 package square wonton wrappers

1 egg beaten with 2 tablespoons water, reserved in small bowl