Fill a large saucepan 3/4 of the way up with water and bring to a simmer over medium high heat. When water is simmering, very carefully lower your eggs in with a slotted spoon, careful so they don't crack. Simmer eggs over medium low heat for 12 minutes careful not to let water to boil.
While eggs are cooking, prepare an ice bath. In a medium bowl, fill it with plenty of ice and water. When eggs are finished cooking, carefully transfer them with a slotted spoon into the ice bath. Set aside until completely cooled.
Peel eggs and run them under cool water to remove and shell fragments. Dry well. Slice each egg vertically, wiping your knife blade in between to keep whites clean. Transfer yolks to a medium bowl or food processor.
Add in remaining ingredients and stir or blend together until very smooth and combined. Transfer mixture to a piping bag or plastic bag with the bottom corner snipped. Chill piping bag and egg whites on your serving platter until ice cold and ready to serve.
When ready to serve, remove platter of egg whites and piping bag from fridge. Gently pipe filling to fill up each egg white center. You will have leftover egg whites for snacks. Garnish with plenty of finely grated pecorino romano, more fresh-cracked black pepper and picked thyme leaves. Enjoy!