Preheat oven to 200F.
In a bowl of a stand mixer, fitted with the dough hook attachment, add milk, yeast, and honey.
Add egg, butter, flour, and salt. Knead the dough on low for 2 minutes, then increase to medium-high and knead for 5 more minutes.
Transfer dough to lightly greased large bowl. Cover dough with plastic wrap and allow dough to rest for 10 minutes.
Flour a clean work surface, then roll dough out into a 12×18 inch rectangle. Spread the softened butter over the dough. Sprinkle herbs evenly over dough, then sprinkle cheese evenly over dough.
Roll dough up tightly into log. Using a serrated knife or unflavored dental floss, cut rolls into 1 ½ to 2-inch-thick slices. You should have 12 rolls. Place into lightly greased 9×13 inch baking dish and cover with plastic wrap. Turn the oven off and place baking dish in oven to rise for 20 minutes.
After 20 minutes, remove plastic wrap. Pour 1/3 cup milk over rolls, then place back in oven, uncovered. Turn the oven on, while rolls are in oven, to 375F. Bake for 18-20 minutes, or until golden brown on top.
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