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Step 1
For the wet ingredients, take room temperature milk, add vinegar and vanilla extract to it. Stir and keep aside.
Step 2
Into the bowl of a stand mixer, add bread flour, sugar, salt, and mix well. Now add the starter and all the wet ingredients.
Step 3
Place the bowl under the stand mixer and start kneading at low speed. Keep kneading for 7 to 8 minutes or until the dough comes together. The dough will be sticky initially but will come together as a smooth dough towards the end. Feel free to add one to two tablespoons of flour if needed but abstain from adding too much flour. Instead, knead more for achieving a smoother dough.
Step 4
Now start adding butter cubes one at a time. Let it mix completely with the dough before adding another cube. Repeat till all the butter is incorporated. You should get smooth dough towards the end of kneading.
Step 5
Transfer the dough to a greased bowl and cover with a cling wrap. Keep the bowl in a warm corner of your kitchen until the dough doubled in size. It may take three to six hours depending on the ambient temperature of your kitchen.
Step 6
When the dough has doubled in size take it out onto a flour-dusted working surface. The dough into 11 to 12 equal pieces (depending on the size of your loaf pan). Use a weighing scale to make equal portions if possible.
Step 7
Shape each piece into a round by tucking the edges and sealing all the edges under to form a smooth top.
Step 8
Grease a 9x5 inch loaf pan and transfer the rounds into it. Place the rounds at least one inch apart giving appropriate space for rising.
Step 9
Give them a spray of warm water and keep it aside for rising in a warm corner of the oven. Alongside place a pan of boiling water. It will prevent the surface of the dough from getting dry and will also provide appropriate moisture and temperature for yeast activity.
Step 10
In a small bowl combine milk and honey for the milk wash.
Step 11
When the dough has risen well above the rim of the loaf pan (about an inch above) preheat the oven to 375 0 F.
Step 12
Bake the sourdough Brioche for 15 minutes before taking them out for a milk wash. Give them a generous milk wash to cover the tops evenly. Put back to bake for 20 minutes.
Step 13
Then towards the end reduce the temperature to 350 0F. Bake for 10 more minutes or until the tops become deep brown.
Step 14
Let the brioche bread cool in the pan for 10 minutes before transferring to a cooling rack.
Step 15
Brioches are best enjoyed warm!