In a large bowl, whisk together the first four ingredients. In a medium bowl, whisk together the remaining three. Combine the two mixtures and stir until well blended.
On a lightly floured surface, knead the dough for about 10 minutes. Add a little flour if the dough is sticky. Place it in an oiled bowl and turn to coat. Cover the bowl with a damp towel and let the dough rise until doubled in size, about 1 1/2 hours.
Line two baking sheets with parchment paper. Punch down the dough and knead it for a few minutes to release the gas bubbles. Halve the dough; return one portion to the bowl and cover. On a lightly floured surface, roll out the other half into a 4 1/2- by 8-inch rectangle.
Cut the dough rectangle lengthwise into six 3/4-inch strips. Cover them with plastic wrap. On a clean surface and working with one at a time, roll and stretch a strip into a 19-inch-long rope. Form a shamrock as shown, then place it on the baking sheet and cover it with plastic wrap. Repeat with the remaining dough, placing six rolls on each baking sheet and spacing them 2 inches apart. Let the dough rise for 45 minutes.
Heat the oven to 350°. Brush the rolls with melted butter. Bake, switching each pan's position halfway through, until the rolls are golden brown, about 25 minutes. Let them cool slightly on a rack before serving.