Crispy Parmesan and Pesto Egg in a Bagel

1. Make sure the bagel's hole is 3/4 inch wide. Use your fingers to pull the hole bigger, if needed. 
2. Heat the olive oil in a skillet over medium heat. Add the the top bagel half, cut side facing up, to one side of the skillet. To the other side, sprinkle 1/2 of the cheese in a circle the size of your bagel. Spoon 1/2 the pesto over the cheese. When the cheese melts, about 1 minute, flip the bagel, cut side facing down, onto the cheese. Crack 1 egg into the bagel hole. Season with salt and pepper. Cover and cook, until the whites are set, but the yolk is still runny, 6 to 8 minutes, or to your preference. Repeat with the remaining bagel half. 
3. In a bowl toss together the avocado, arugula, dill, lemon, sesame, chili flakes, and salt. Serve with the bagel.