Bring a large pot of well-salted water to a boil and cook pasta to al dente according to packet instructions.
Wipe out the skillet from the pangritata, add 1 Tbsp olive oil and 1 Tbsp butter and melt together over medium heat.
Add the garlic and immediately break the eggs into the skillet. If need be, lower the heat a bit. You want the garlic to cook without burning and the egg whites to set, but the yolks to remain runny ooey gooey.
Drain the pasta well, reserving ½ cup (with a mug) of the cooking liquid. This is the best thing Jamie Oliver ever taught me.
Add pasta back to the pot, pour over the eggs and all the fat from the skillet, add the parsley and capers and toss well, breaking up the eggs as you do. Add in some of the reserved cooking water to combine all the ingredients.
Plate the pasta and eggs, season well with freshly ground black pepper, sea salt, sprinkle with the grated cheese and then top with the pangritata. Enjoy!