Mix dry ingredients:
Begin the day prior to baking. In a stand mixer bowl with dough hook attachment, whisk together white bread flour and all-purpose flour. Add yeast on one side, salt and sugar on the other; stir until blended.Add wet ingredients:
Pour in aquafaba, non-dairy milk, and vanilla extract; mix until a shaggy dough forms. Knead on medium speed until smooth and stretchy. If kneading by hand, do so on a surface without extra flour.Incorporate fat:
Incorporate softened vegan block butter or olive oil, mixing until fully integrated and dough becomes smooth again; the dough will be soft and sticky. Hand mixing (in a bowl, not on a surface if using olive oil) may be easier. Persist as it takes time to combine.Refrigerate overnight:
After fat is thoroughly mixed, continue kneading until dough cleans the bowl sides (still soft and sticky). Transfer dough to a bowl, cover, and refrigerate overnight for its first rise.Prepare loaf pan:
The following day, dough should have at least doubled. Line a 2–2½ lb loaf pan (roughly 11.5 x 21.5 cm / 4.5 x 8.5 in; a 13 x 23 cm / 9 x 5 in pan also works) with parchment paper.Divide dough:
Deflate dough. For a standard loaf, shape into a log and place in pan. For a pull-apart loaf (as shown), cut dough into 6 or 8 equal pieces (8 recommended).Shape dough balls:
Form each piece into a taut ball: gather edges to center, pinch shut, flip onto a lightly floured surface, cup hand around ball, and gently roll to smooth. Repeat for all pieces.Arrange in pan:
Place balls in two rows inside the loaf pan, pressing together to fill.Second rise:
Cover loosely and let rise until doubled, about 1–2½ hours depending on temperature. Ready when puffy and a gentle finger poke leaves a slow spring-back. If it rebounds quickly, let rise longer; if it collapses, deflate, reshape, and re-ris.Make glaze:
When loaf is almost ready, preheat oven to 180°C/350°F (175°C)/gas 4. Make glaze by whisking 1 Tbsp non-dairy milk, 1 Tbsp maple syrup, and ½ tsp oil in a small bowl.Brush glaze:
Brush loaf gently with some glaze; avoid letting it drip down sides (which can cause sticking and hinder rising).Bake loaf:
Bake for 20 minutes, then brush with more glaze. Lower oven to 160°C/320°F (160°C)/gas 3 and bake another 25–30 minutes until internal temperature hits 94°C/201°F (95°C) on a probe thermometer, or a skewer inserted in center comes out clean. If top browns too fast, tent loosely with foil.Cool and store:
Cool in pan for 15 minutes, then turn out onto a wire rack to cool fully before slicing. Store in an airtight container.