In a large mixing bowl or the bowl of a stand mixer fitted with a hook attachment, combine the yeast and warm water. Stir it around, then let sit for 5 minutes until the mixture is foamy. Add flour, sugar, olive oil, and salt. Mix by hand or with the dough hook on low speed for 1 minute. Once all of the ingredients are mixed, slowly knead for 7 minutes by hand or with your dough hook on low-medium speed. If your dough is too wet, add up to 1/4 cup more flour. After kneading, your dough should be smooth and elastic. Poke it with your finger – if it slowly bounces back, your dough is ready to rise. If not, keep kneading.
Shape the dough into a ball and place in a large mixing bowl that has been greased lightly with olive oil. Turn it over to coat all sides. Cover tightly with plastic wrap and allow to rise in a warm environment (about 75°F or 80°F/ 24°C or 27°C) for 1 hour or until doubled in size.
Preheat oven to 400°F (204°C). Line 2 large baking sheets with parchment paper or silicone baking mats.
Once risen, punch the dough down to release the air. Turn the dough out onto a lightly floured surface. Using a sharp knife or dough cutter, slice dough in half. Then slice each half into quarters. You’ll have 8 pieces of dough. Flatten each piece with your fingers or use a rolling pin. You want each piece of flattened dough to be about 6 inches long and 4 inches wide. Transfer flattened dough to lined baking sheets. Place the cheese and ham on top of the dough on one side, then fold the other side over top. Pinch the edges to seal as best you can. Use a fork to crimp the edges. Brush the tops and sides of each pocket with egg wash, then slice 2-3 slits in the tops for air vents (use a super sharp knife to do this).
Bake the pockets for 20-25 minutes, or until the tops are golden brown. Make sure to rotate the baking sheet once or twice during bake time. Remove pockets from the oven and allow to cool on the pan until ready to handle and serve.