Begin by slicing your small sandwich rolls in half and separating the top from the bottom (set the tops to the side to be used later).
Next, carefully pull out the excess bread from the bottom half so that you create a divot in the bun.
Stuff the divot with shredded cheddar cheese, then take a handful of your ground italian sausage and cover the cheese with it. Make sure to spread out the ground sausage all over the bread so it completely covers the cheese.
Once done, set that to the side and begin working on the next roll until all the rolls are completed.
Once all the rolls are done, place them in the fridge for 15-20 minutes to firm up.
In another bowl, mix together all the ingredients for the chimichurri sauce. Set to the side.
Preheat a medium heat fire (around 325F) for direct grilling.
Take out the bread and place it over the coals with the sausage face down.
Cook over the heat for about 15-17 minutes until the sausage is 165F internal or completely cooked through. If you have flare ups, make sure to move the bread around in order to prevent them.
Once done, pull the sausage bread off and keep warm until ready to use. At this time, add the top buns to the grill and cook till they are nice and golden brown.
When the bread is done cooking, kick up the heat to 375F and add a cast iron skillet with oil to the grill.
Fry up some eggs (one for each sandwich) and cook them to your liking. Once done, pull off and set to the side.
Serve the Cheese Stuffed Sausage Sandwich with a fried egg, some chimichurri, mayonnaise and the top bun. Enjoy!