In a saucepan, melt 3 tablespoons of the butter. Add the milk and sugar and heat just until warm. Transfer to a large bowl, stir in the yeast and let stand until foamy, 5 minutes. Stir in the flour and 1 1/2 teaspoons of salt until a sticky dough forms. Turn the dough onto a lightly floured work surface and knead until smooth, 5 minutes. Oil the bowl and return the dough to it. Cover with plastic and let stand in a draft-free spot until doubled in bulk, about 1 hour.
Butter a 10-inch tube or Bundt pan. Punch down the dough and divide it into 4 pieces. Roll each piece into a 12-inch log and cut each log in 12 equal pieces. Roll each piece into a ball.
Heat 1 tablespoon of the butter in a skillet. Add the onion and cook over moderate heat until softened, 6 minutes. Stir in the mustard, chives and thyme. Add the remaining 4 tablespoons of butter; stir until melted. Season lightly with salt and transfer to the large bowl to cool slightly. Add half of the dough balls and turn to coat with the onion mixture. Arrange the balls in the bottom of the pan. Repeat with the remaining dough balls. Cover loosely with plastic wrap and let stand until risen to the top of the pan, about 1 hour.
Preheat the oven to 425°. Bake the bread in the lower third of the oven for 25 minutes, or until golden. Cover the pan loosely with foil, reduce the oven temperature to 375° and bake for 30 minutes longer, or until risen. Let the bread cool in the pan for 15 minutes. Set an inverted plate on top and turn the bread out onto it. Set another plate on top and invert the bread so it's right side up. Break into rolls or cut into slices.
The bread can be prepared through Step 3 and refrigerated overnight.
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