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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess.
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To make the dough: In a stand mixer or bread machine (programmed for dough), mix together all of the ingredients to form a smooth, shiny dough. Don't worry; what starts out as a sticky mess becomes beautifully satiny as it kneads. This dough takes longer than most to develop, so be prepared to let the dough knead for up to 15 to 20 minutes in a stand mixer. Also, we don't recommend trying to knead it by hand. If you're using a bread machine, let it complete its kneading cycle, then continue as directed below.
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Form the dough into a ball (it'll be very soft), place it in a greased bowl, cover the bowl, and it let rise for 1 hour. Then refrigerate the dough for several hours, or overnight. This will slow the fermentation and chill the butter, making the dough easier to shape.
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Divide the chilled dough into 12 pieces to make mini-brioche (brioche buns); leave it whole for one large round brioche; or divide it in half for two 8 1/2" x 4 1/2" loaves.
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Place the dough into the greased pan(s) of your choice, cover lightly, and let rise for 2 1/2 to 3 hours, until it's doubled and looks very puffy. If you're making two loaves, it's fun to make simple three-strand braids, and set them in the loaf pans.
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To bake a large, round brioche: Place the pan into a preheated 400°F oven. After 10 minutes, reduce the oven heat to 350°F and bake for about 30 to 35 minutes more. Check the brioche after 15 minutes; tent with aluminum foil if it appears to be browning too quickly. Brioche should be a deep brown when done, should sound hollow when tapped, and will read 190°F at the center using an instant-read thermometer. (It's easy to underbake since it browns so quickly!) Remove the brioche from the oven, and after 10 minutes remove it from the pan to cool completely on a rack.
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To bake the mini brioches: Place the pan(s) onto a baking sheet for easy handling, as shown; then nestle that baking sheet into another baking sheet, to protect the buns' bottoms from over-browning. Bake the buns in a preheated 375°F oven for 25 to 30 minutes (tent after 10 minutes if they're browning too quickly). Remove them from the oven, let stand for 5 minutes, then turn them out onto a rack.
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To bake the loaves: Allow the loaves to rise until they've nearly reached the rim of the pan, about 3 hours. Set the loaf pans on a baking sheet, for easy handling. Bake in a preheated 350°F oven for 30 to 35 minutes, tenting with foil after 15 to 20 minutes. Bake until the internal temperature reaches at least 190°F in the center, and up to 205°F for a crustier loaf.
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To make the glaze: Combine the confectioners' sugar, vanilla, and salt. Add enough cream to make a pourable consistency. Drizzle the glaze over the baked loaves, if desired.
