Add the potatoes, rosemary and a generous pinch of salt to a large pot. Add enough water to cover the potatoes. Bring to a boil and cook until the potatoes are tender and can be easily pierced with a fork, about 15 minutes. Reserve 1 cup of the potato cooking water. Drain the potatoes.
Spread the potatoes out on a sheet pan to let cool slightly. While they are still warm, slice the top one-quarter to one-third off each potato lengthwise, and if needed, cut a tiny sliver off the bottom of each to allow them to rest level on a plate. Put the cut-off parts of the potatoes into the bowl of a food processor fitted with a blade attachment.
Add the mustard, yogurt, lemon zest, lots of black pepper and some of the reserved potato water to the food processor. Pulse until coarsely pureed, adding more potato water as needed. (You may need 1/2 to 1 cup of the water.) Be careful not to overprocess or the mixture will become gluey. Adjust the salt if necessary. Transfer the filling to a piping bag or gallon zip-top bag. Slice a 1/2-inch opening in the piping bag or slice off the corner of the zip-top bag.
Transfer the boiled potatoes, cut-sides up, to a deviled egg plate or serving platter. Top each prepared potato with an equal amount of filling. Garnish with the chives and paprika. Serve at room temperature or chilled.