Warm broth in a saucepan over low heat. Meanwhile, beat room temperature eggs until they are frothy, then slowly incorporate lemon juice until fully combined.
Remove the broth from the heat when it is hot but not boiling, then allow it to cool for 2-3 minutes. Then, while vigorously beating the egg mixture in a medium bowl, begin to ladle in small spoonfuls of broth until consistent.
Add avgolemono sauce back to the pot, then mix in cornstarch, stirring constantly over low heat until thickened and evenly warmed. Do not allow it to boil.
Remove from stove and serve.
Notes
I recommend using an immersion blender because it helps prevent the sauce from curdling by evenly incorporating the hot broth into the egg mixture, while also smoothing out any small bits of cooked egg.
Stir the mixture with a spoon, rather than a whisk once it's on the stove to minimize excess froth. You can remove any excess foam with a fine mesh skimmer.
If using an immersion blender, try to keep it submerged and avoid moving it up and down. This will keep it from getting too foamy.
You could use a hand mixer or even a whisk instead of an immersion blender; just be extra careful to mix consistently.
The order in which the ingredients are added should not be altered for this recipe.
It's important to add the broth gradually, rather than all at once, as this will allow the egg mixture to slowly increase in temperature, preventing curdling.
Store leftover avgolemono sauce in an airtight container in the fridge for 2-3 days.
Reheat over very low heat, stirring often. Do not allow it to come to a boil, or it will curdle.