Warm the soy milk in a microwave-safe bowl or cup in 15-second intervals until warm but not hot (105-110°F). Combine with the maple syrup and yeast in a bowl or cup. Let stand for 5-10 minutes, until foamy.
Add the olive oil, both flours, salt, and yeast mixture to a mixing bowl. Stir until a shaggy dough forms. Cover and let rest for 20 minutes to give the flour time to absorb the liquid.
Knead on a lightly floured surface for 8-10 minutes, until smooth and elastic. The dough should feel slightly tacky. Use lightly oiled hands if needed to prevent sticking. If the dough feels dry or stiff, knead in extra soy milk 1 teaspoon at a time; add extra flour sparingly, only if the dough is too sticky to handle.
Place the dough in a lightly oiled bowl, turn to coat, and cover. Let rise in a warm spot for 60-90 minutes, or until roughly doubled in size.
Lightly grease a 9×13-inch baking dish. Gently deflate the dough and divide it into 12 equal pieces. Pull the edges of each piece underneath to form a smooth ball, pinch the seam closed, and arrange seam-side down in the dish.
Cover and let rise for 45-60 minutes, until noticeably puffy. Toward the end of the rise, preheat the oven to 375°F.
Brush the rolls lightly with soy milk and sprinkle with everything bagel seasoning, if using. Bake for 20-25 minutes, until golden brown and the center rolls are cooked through.
Let rest in the pan for 5 minutes, then transfer to a wire rack. Cover loosely with a clean kitchen towel as they cool for a softer crust.