Stir bread flour, whole wheat flour, and salt together in a large bowl until well combined; set aside.
Gently whisk 1 1/4 cups warm water and yeast together in a small bowl. Allow to rest at room temperature until foamy and fragrant, about 10 minutes.
Make a shallow well in the center of the flour mixture, and pour in the yeast mixture. Stir together using a spatula until a coarse dough begins to form. Transfer dough to a lightly floured work surface and begin kneading, dusting with more flour as needed to prevent dough from sticking, until smooth and elastic, about 10 minutes.
Shape dough into a ball and place in a large bowl lightly greased with cooking spray. Cover the bowl with a towel lightly dampened with warm water and set aside in a warm spot to rise until doubled in size, about 2 hours.
Lightly grease a 7- to 8-inch round cake pan with cooking spray and line the bottom with parchment paper; lightly grease parchment paper with cooking spray; set aside.
Using your fingers, gently press down on dough to deflate slightly and transfer to a work surface that has been very lightly dusted with flour. Gently knead dough 2 or 3 times, preserving as many air bubbles as possible. Using the sides of your hands, shape dough into a ball by pulling the sides under until a smooth and slightly shiny surface develops. Gently transfer dough to the prepared cake pan and lightly dust with flour; cover tightly with aluminum foil.
Add remaining 1 cup water and a steam rack to a multi-functional pressure cooker (such as an Instant Pot®); place cake pan on the rack. Close and lock the lid. Turn vent to Sealing position. Select Manual/Yogurt setting; set timer for 1 hour. Dough will rise in cooker and double in size. Press Cancel.
Meanwhile, preheat the oven to 450 degrees F (230 degrees C).
Select Manual/Pressure Cook setting on the Instant Pot®. Select high pressure according to manufacturer’s instructions; set timer for 40 minutes. Allow 3 to 5 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer’s instructions, 8 to 10 minutes. Unlock and remove lid. Carefully remove the cake pan as it will be hot; remove aluminum foil.
Transfer cake pan to the preheated oven and bake until bread is golden brown, about 20 minutes. Remove bread from the cake pan and transfer to a wire rack to cool completely before slicing, about 30 minutes. Using a bread knife, slice loaf crosswise into 3/4-inch thick slices.
Times, instructions, and settings may vary according to cooker brand or model.
Using the yogurt setting creates an environment similar to a proof box and allows the dough to have a warm, cozy place to develop during its final rise.
The cake pan is necessary! Even if you get a burn warning, the bread doesn’t actually burn. The burn warning is issued simply because the bread is developing a crust on the bottom of the loaf and the program recognizes the sticking of the crust as something burning. Placing the bread within a cake pan lined with parchment paper creates a barrier and allows the bread to successfully bake without the risk of burning.
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