Step 1In a large bowl, whisk together the flour, yeast, salt and ground caraway.
Step 2In a small saucepan, gently heat the milk over low heat until it is lukewarm. Remove from heat and set aside.
Step 3To the large bowl of dry ingredients add the egg, softened butter and milk, and mix until thoroughly combined to form the dough. Knead the dough in the bowl until it is soft and smooth, 5 to 7 minutes. (It will be sticky and messy at first but will come together as it is kneaded and should not need extra flour.) Leave the dough in the bowl and loosely cover with a towel or plastic wrap. Set aside until doubled, 40 minutes to 1 hour (depending on the temperature of the kitchen).
Step 4Divide the dough into 6 pieces in the bowl. Remove 1 piece of the dough and place it on a large, flat workspace. (Keep the rest of the dough covered in the bowl.) Roll the dough into 1 long strip about one-half inch wide. (If your workspace is not large enough, cut the dough into smaller pieces to roll shorter strips.) Cut the strips into 4-inch lengths.
Step 5Combine 2 strips to form a cross, and place on a baking sheet. Continue rolling and cutting the dough until all of the dough has been formed into crosses, spacing them 1 1/2 to 2 inches apart.
Step 6Loosely cover the baking sheets with plastic wrap and set aside until puffed and risen, about 30 minutes. Meanwhile, heat the oven to 475 degrees.
Step 7Gently brush the crosses with beaten egg or egg yolk (beaten egg yolks will give the rolls deeper color than beaten whole egg), and sprinkle a few caraway seeds on top of each cross. Bake until puffed and golden, 6 to 10 minutes.