Put potatoes in a large heavy saucepan with bay leaves, salt to taste, and enough water to barely cover. Bring to a boil, covered. Reduce heat and simmer potatoes until just tender, 10 to 15 minutes.
Drain all but 1/4 cup water from potatoes. Add peas (rinse with cold water if frozen) and salt to taste. Cook over medium-heat until peas are just tender and warmed through, about 7 minutes for fresh peas and 5 for frozen. Drain. Stir in half of butter and grind in pepper.
Serve hot, topped with remaining butter.
Make ahead: For potatoes, a few hours (keep them in the pot and tip out most of the water). Add peas and reheat.
*Mediterranean bay leaves, the traditional type used in cooking, have an oval shape and milder flavor than California bay leaves, which are long and pointed and have a pungent flavor.