In a small bowl, mix the 1 teaspoon active dry yeast, 1 tablespoon sugar, and ⅔ cup lukewarm water together. Let it rest for 10 minutes, until it dissolves and starts bubbling. If it doesn't foam, the yeast is dead and you'll need fresh.
Add the 3 cups all purpose flour, 1 teaspoon salt, ½ cup melted butter, 2 eggs, and the yeast mixture to the bowl of your mixer. Mix for about 5 minutes, until the dough is soft but not sticky. If it clings to the bowl, add a little more flour and keep mixing until it pulls away cleanly.
Place the dough in an oiled bowl, cover with plastic wrap, and let it rise in a warm place until doubled in size, about 1 hour.
Preheat the oven to 350°F and line a baking sheet with parchment paper.
Roll the dough out on a lightly floured surface into a rectangle about 14 by 18 inches and ¼ inch thick.
Sprinkle all the 2 cups shredded cheddar over half the dough, leaving a small border. Lay the 8 slices of ham over the cheese. Fold the empty half of the dough over the filling and press down gently.
Cut the folded dough into 8 equal pieces and transfer them to the prepared baking sheet, spaced apart.
Brush the tops with the beaten egg, then sprinkle with the ¼ cup grated Parmesan and 1 tablespoon dried parsley.
Let the pockets rest and rise on the tray for about 30 minutes.
Bake for 20 to 25 minutes, until deeply golden. Some cheese will bubble out of the cut edges and that's normal. Let them cool for 5 minutes before serving.