A nonstick skillet is crucial so the potatoes don’t stick to the pan as the liquid evaporates.
Trim the potatoes of any eyes or damaged areas and wash well in cold water. Arrange as many potatoes as will fit in one layer in a 10-inch nonstick skillet (there should be a little room to spare; save any extra potatoes for another use). Add the rosemary, broth, oil, butter, and salt. Bring to a boil over high heat. Reduce the heat to medium, cover the pan but leave the lid a tad ajar, and boil until the potatoes are tender when pierced with a fork, about 20 minutes. The liquid should still halfway surround the potatoes; if it doesn’t, add more broth or water until it does.
Remove the pan from the heat and press on each potato with a 1/4-cup measure just until it cracks open. Set the pan over medium-high heat and cook, uncovered, until all the liquid has evaporated and the potatoes have browned on one side, about 10 minutes. Gently turn the potatoes and brown the other side, another 4 to 5 minutes.
Press firmly on the potatoes to crack them; this helps them absorb more broth and ensures a creamy, moist interior. Then continue boiling, but now uncovered.
After the broth has completely reduced, let the potatoes sizzle in the skillet until their bottoms are deliciously browned. Turn to brown the other side and then serve while hot.
Remove the pan from the heat and let the potatoes rest for 5 minutes before transferring them to a serving platter. Sprinkle with the chives and serve immediately, passing the fleur de sel so diners can sprinkle some on if they want.