Bring the Chicken Stock to a gentle simmer in a medium pot.
Stir in the Medium-Grain Rice, reduce the heat to low, and cook partially covered until the rice is tender and the soup has slightly thickened (about 15–20 minutes).
Season the cooking liquid with a generous pinch of Fine Salt, tasting and adjusting as needed.
While the rice cooks, whisk the Eggs in a medium bowl until frothy, then whisk in the juice of the Fresh Lemons until smooth.
Temper the egg-lemon mixture by slowly whisking in 1–2 ladlefuls of the hot broth from the pot until the mixture is warm and glossy.
Turn the heat to very low or remove the pot from the heat and slowly pour the warmed egg-lemon mixture back into the soup, whisking constantly to prevent curdling.
Return the pot to the lowest heat just long enough for the soup to thicken slightly (do not boil), then remove from heat and taste for seasoning.
Finish with freshly ground Black Pepper and additional salt if desired, ladle into bowls, and serve warm.
