Sauté sliced shallots over medium-high heat in a cast-iron skillet for 7-10 minutes or until softened and beginning to brown. Remove pan from heat. The residual heat will continue to cook the shallots further and deepen their flavor.

Separate yolks from whites by cracking the egg on your work surface, balance egg inside one half of the shell, then gently pour egg into your other hand, cupped. Spread your fingers just enough to allow the white to pass through (catching the whites in a container placed underneath - save for another use). Carefully pass the egg back and forth between your hands until the yolk is completely freed of the white. Slip the yolk into a small bowl and repeat with remaining eggs.

Heat stock over medium-low heat in a large saucepan. Add to it the grated garlic and stir to incorporate. While stock warms, blend lemon juice, zest, and yolks together in a high-speed blender until uniform and creamy.

Once stock is hot but not boiling, turn heat off. Transfer a few ladlefuls to a spouted measuring cup. With the blender running on medium/ medium-low, pour stock in a bare drizzle until fully incorporated, pausing halfway through to scrape down the sides as needed. This method of adding the hot stock gradually tempers the eggs without scrambling them, and creates a lush body for the soup.

Gradually pour tempered egg mixture into warm stock while whisking to combine. Add salt and pepper and stir, adjusting seasoning as necessary. Whisk soup for an additional 2-3 minutes and simmer until slightly thickened.

Set a pot of water to boil and cook orzo al dente, according to package instructions. Drain and set aside.

Assemble a pile of orzo, shallots, and chicken into each bowl, then ladle hot broth on top. Alternatively, you may add the shallots, chicken, and orzo directly to the soup for a more homogenous result. If using this method, stir well to incorporate. Garnish avgolemono with freshly cracked black pepper and a generous amount of dill. Serve immediately.