How to Make It
Make the rolls In the bowl of a stand mixer fitted with the dough hook, whisk the warm milk, yeast and sugar and let stand until foamy. With the machine at medium-low speed, beat in the flour, caraway seeds, 2 tablespoons of butter and the salt. Knead the dough until smooth but a little tacky, 5 minutes. Transfer to a lightly oiled bowl, cover with plastic wrap and let stand in a warm place until doubled in bulk, 1 hour.
Meanwhile, make the butter In a small saucepan, melt the butter with the garlic. Scrape into a medium bowl and let cool, then stir in the parsley.
Butter a 12-inch cast-iron or nonstick skillet. Divide the dough in half; keep 1 piece covered with a kitchen towel. Cut the other into 8 pieces; form each into a ball, then roll in the garlic-parsley butter. Arrange in concentric circles in the prepared skillet about 1/4 inch apart. Repeat with the second piece of dough. Cover loosely with plastic and let stand in a warm place until doubled in bulk, 1 hour.
Preheat the oven to 350. Brush the rolls with more of the butter and bake for about 30 minutes, until golden. Brush with the remaining butter, sprinkle with sea salt and serve.