Preheat your oven to 150°F or as low as your oven will go. If youre oven runs warmer, stick some oven mitts in the door to keep the oven slightly open and lower the temperature.
Pour the olive oil into a cocotte about 1 inch up the top. Season with salt and pepper. Place in the oven for 15 minutes. After the oil has warmed, add the egg yolks and cook for 35 -45 minutes, depending on how runny you want your eggs.
The butter:
In a bowl, combine softened butter with cheese, pepper and salt. Mix until smooth and then using parchment paper, roll butter into a log shape. Chill in the freezer until slightly firm, about 25 minutes.
The rest:
Coat bread in olive oil and cook in a skillet over medium heat for 2-3 min per side.
Spread with butter and top with a confit egg yolk. Sprinkle with more parmesan cheese and that's it! Enjoy!