Warm your water to 110 to 120℉. Then add your cane sugar and yeast then gently mix to combined mix. Set aside and let set for 5 to 10 minutes for the yeast to get bubbly and activate. If after 5 minutes there are no bubbles, your yeast is likely no longer active. Start over with new yeast.
While the yeast is activating, in a large bowl or your stand mixer, whisk together the flour and salt. Then after 5 to 10 minutes, add the water and yeast mixture and the olive oil. Using a rubber spatula, mix until the liquid is absorbed and the ingredients form a sticky dough ball.
Using either your hands or an electric mixer with the dough hook, knead the dough for 8 to 10 minutes. The dough might be sticky at first, but you can add up to ¼ cup flour while kneading to make it easier to manage and for the dough to come together and build tension. You want the end dough ball to be smooth, with slight dimples with a bit of tension formed.
After you have kneaded your dough, lightly grease your dough ball of dough with some additional oil and place it back into the bowl in a ball. Cover the bowl with plastic wrap or a kitchen towel and let it sit for at least 1 hour on the counter in a warm area. The dough should rise and double in size.
After an hour or once your dough has doubled in size, punch down the dough and remove it from the bowl.
Divide the dough into 10 equal balls, or 8 if you want very large buns, and roll each into a ball. Using your fingers, pinch and pull the undersides to shape each a round ball.
Using 1 or 2 baking sheets, lined with parchment paper or silicone baking mats, line up your small dough balls, about 4 inches apart if you don't want them to spread into one another / touch while rising or baking.
Cover your baking sheets and dough balls with a light kitchen towel and allow the balls to rise for another 45 minutes. During the last 20 minutes of the rise, preheat your oven to 400℉. Also, make your egg wash, add your plant-based milk, maple syrup or agave, and mustard in a mixing bowl, and mix to combine.
Using a pastry brush, brush your vegan egg wash over the buns and the sides. Sprinkle some sesame seeds over the top, if using.
Bake your buns for 15 minutes. Remove, and allow to cool on the baking sheet for about 5 minutes, then transfer to your cooling rack and allow the buns to fully cool. Do not try to slice the buns while they are still hot. Note the buns will also soften as they cool.
Slice, tear, slather in butter, enjoy any way you want! I really love using these buns with my black bean burgers*!