Place potatoes in a pot and cover with lightly salted cold water. Bring to a boil; cook until crisp-tender, 1 to 2 minutes. Drain, pouring enough hot cooking liquid over peas to cover. Let peas stand 30 seconds, then drain and rinse peas under cold water.
Melt butter in a large skillet over high heat. Add peas, potatoes, broth, and salt. Cook, stirring, until liquid reduces to a glaze, 5 to 7 minutes.