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1
Bring the lamb broth to a full simmer in a wide saucepan. Taste and adjust salt: the broth must be fully seasoned at this stage, as the egg mixture will dilute its intensity. Reduce the heat until the surface barely trembles — the broth must be hot but not boiling. Judge by sight: small, lazy bubbles rising at the edge, no violent agitation.
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2
Beat the whole eggs thoroughly in a bowl until yolks and whites are fully combined. Add the finely grated Pecorino Molisano, the shredded fresh mint, and the black pepper. Beat again until the mixture is homogenous. The scent of fresh mint should be immediate and pronounced — this is the defining perfume of the dish.
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3
This is where the dish lives or dies. With one hand, pour the egg mixture into the barely simmering broth in a fine, steady thread; with the other, stir the broth gently and continuously in a slow circular motion. The egg must meet the hot broth in small quantities at a time — never all at once — so that it cooks into long, irregular, silky wisps rather than lumps or a scrambled mass. The correct result is visible: thin, pale-gold wisps suspended throughout a clear broth, neither collapsed into fragments nor clotted.
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4
Remove from heat immediately once all the egg mixture has been incorporated and the wisps have set. Touch the surface gently with a spoon: the wisps should feel barely firm, not rubbery. Serve at once — the egg wisps toughen within minutes if left in the hot broth.
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5
If following the rustic Molisano tradition, place a slice of stale bread in each warm bowl before ladling the soup over it. Finish each portion with a grating of aged Pecorino Molisano at the table.