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To make the dough: In a microwave-safe measuring cup or bowl, combine the milk, butter, sugar, and salt. Heat, stirring occasionally, until the butter melts. (Alternatively, combine the ingredients in a saucepan and cook over low heat until the butter melts.) Let the mixture cool to lukewarm.
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While the mixture cools, weigh 4 cups (480g) of flour; or measure it by gently spooning it into a cup, then sweeping off any excess.
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Transfer the cooled milk mixture to a mixing bowl, and add the eggs, yeast, flour, and potato flour and mix to form a shaggy dough. Knead the dough — using your hands, a stand mixer, or your bread machine set on the dough cycle — until it's smooth. The dough will remain somewhat sticky, but should definitely form a ball. During the summer, or in a warm/humid climate, you'll probably find you have to add the remaining 1/4 cup (30g) flour.
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Place the dough in a greased container, cover, and let it rise for about 90 minutes, until it's puffy though not necessarily doubled in bulk.
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To make the filling: While the dough is rising, place the filling ingredients in a bowl and mix to combine.
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After the dough has risen, deflate it and divide it in half. Working with one piece at a time, place the dough on a lightly greased or lightly floured surface (your preference), and roll/pat it into a 12" circle about 1/4" thick. Cut 3 1/2" to 4" circles with a cutter, large canning jar lid, or English muffin ring; you should have about 10 circles.
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Spread the butter-herb filling on half of each round, fold in half, and place fold-side down in a lightly greased 8 1/2" x 4 1/2" loaf pan. Repeat with the remaining half of the dough, filling another 8 1/2" x 4 1/2" bread pan. Or place all of the rounds in a 12" x 4" x 2 1/2" tea loaf pan. Shape any scraps into small rolls; or butter them and pile them into the wells of a muffin pan. They won't look pretty, but they'll taste just fine.
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Cover the pan(s) with greased plastic and let the dough rise for about 1 1/2 hours, until it's puffy and starting to fill the pan. Toward the end of the rising time, preheat the oven to 350°F.
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Uncover the loaves and bake them for 25 to 30 minutes. Bread baked in a ceramic pan will take 5 to 7 minutes longer to bake than in a metal one. Tent the loaves with foil if they look like they're browning too quickly.
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Remove the bread from the oven; brush it with additional melted butter, if desired. Turn the loaves out of the pan, and serve warm.
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Store any leftovers, well wrapped, at room temperature for several days; freeze for longer storage.
