In a small bowl, combine the chopped hard-boiled egg, parsley and garlic. Season the insides of each cutlet with some salt and freshly ground black pepper and divide the egg mixture evenly between the four pork cutlets, placing it on one half of the cutlet and leaving some space around it. Top each dollop of filling with two half moons of smoked mozzarella. Fold the other half of the cutlet over the filling and use your meat mallet to pound the edges together a little to seal the pocket shut. Cut away any excess meat that you pounded around the pocket. Season the outside with salt and freshly ground black pepper and coat it lightly in flour.
Fill a pot with about an inch of water and put it over high heat to bring it to a boil. Place a large skillet over medium high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Cook the stuffed pockets in the pan until golden brown and cooked through, 2-3 minutes per side. Remove the pockets from the pan to a plate and cover them with aluminum foil to keep them warm.
With your pan still on the heat, add in the pancetta and cook it until crispy, 3-4 minutes. Add in the onion and cook for another 3-4 minutes until tender. Toss the tomato paste into the skillet next and cook it for about 1 minute until it smells sweet, then pour in the white wine and chicken stock. Bring the liquids up to a bubble and simmer the sauce for a couple of minutes until it has thickened up slightly.
While the sauce is thickening up, toss the broccolini into the pot of boiling water and cover it with a lid. Cook until they're bright green and tender, 2-3 minutes, then drain the water off from them. Add the Parmigiano Reggiano, lemon zest and juice, and some salt and freshly ground black pepper to the pot and give it a good stir to coat.
Serve up the stuffed pockets with some broccolini and a healthy spoonful of your delicious sauce.