emulate
EM-yuh-laytverbMeaning to imitate someone you admire, hoping to match or surpass them
Memory hook EM-U-LATE: “I’ll be like EM, you’ll see, LATEr!”. Little Theo watches his big sister Em stretch up tall before her dance, then copies her move exactly: one day he’ll be as good as Em. He emulates her.
Little Theo emulates his big sister, practicing her cartwheels every afternoon.
In context Jamal did not merely copy his grandmother’s recipes; he tried to emulate her, aiming to cook as well as she did and someday to invent dishes of his own.
Similar imitate, follow, match, rival
From Latin aemulari, “to rival, to try to equal,” from aemulus, “a rival.”