How can someone recognize his brothers if they cannot recognize him? Targum Pseudo-Jonathan on Genesis 42:8 answers with a very physical explanation: the beard.
The mathematics of a face
When Joseph was taken from his family at seventeen (Genesis 37:2), he had no beard. The Aramaic paraphrase, which took its final form in the Land of Israel around the seventh or eighth century CE, puts it plainly: "when separated from them, they had the token of the beard; but they did not recognise him, because (at that time) he had not the token of the beard, and at this hour he had it." His older brothers were already bearded when they last saw him; he was not. Twenty-two years later, Joseph at thirty-nine wears the full Egyptian beard of a high official. They see a shaven-jawed boy in their memory and a bearded governor before them.
The asymmetry that saves the family
The Targum turns the asymmetry into a theological insight. Joseph could recognize them because their beards had grown longer, grayer, but their faces were substantially the same. They could not recognize him because he had grown from boy to man in the interval. Time erases a child's face and sharpens an adult's. The rabbinic tradition reads this detail as providence: if the brothers had recognized him immediately, the whole reconciliation drama — the testing, the return of Benjamin, the final tears — could not have unfolded.
The takeaway
A beard is a small thing, but it bought the family twenty more verses of testing, repentance, and return. Sometimes the providence hides in the most ordinary detail.