Combine the yeast and lukewarm nondairy milk in a stand-mixer bowl and let it bloom for about five minutes.
Add the all-purpose flour, aquafaba, sugar, and salt, and mix on medium speed until incorporated. Add the bread flour and knead for five minutes.
Knead in the olive oil one third at a time, waiting for each addition to absorb before adding the next. Shape the smooth dough into a ball.
Place the dough in an oiled bowl, cover, and let it rise in a warm place for about 90 minutes, until doubled.
Gently shape the risen dough into a loaf and place it in a loaf pan. Let it rise again until puffy, about 30 minutes.
Whisk the maple syrup, aquafaba, and remaining teaspoon of olive oil. Brush the loaf, then bake at 375°F until golden and cooked through, about 30 minutes.
Cool the brioche in the pan briefly, transfer it to a rack, and let it cool before slicing.