In a mixing bowl, add the lukewarm soy milk, yeast, and 2 teaspoons sugar. Stir the mixture briefly and let it stand at room temperature until foamy and creamy, approximately 10 minutes. This step allow the yeast to proof.
In a second mixing bowl, combine the ground flaxseeds and water. Let it stand at room temperature for 5 minutes. Flaxseeds will soak up some of the water.
Add oil and vinegar. Stir briefly.
Dice one peach and cut the other one into slices. Set aside.
Preheat oven to 200°F. Lightly oil 3 mini loaf pans. If you prefer, use parchment paper.
In a third mixing bowl, whisk together all dry ingredients. Pour the wet ingredients into the dry ingredients and mix together with a rubber spatula. Stir just until they are combined.
Carefully fold the diced peaches into the bread dough. The bread dough should be very sticky at this point.
Scoop the bread dough into the prepared loaf pans. Press down the dough with greased palm and then tap the loaf pan on the counter gently to ensure there are no gaps or air pocket in the batter.
Spray the top of the dough lightly with oil. Arrange peach slices on top of the dough. Press in very slightly.
Cover the mini loaf pans with a piece of oiled plastic wrap. Turn off the oven.
Place the loaf pans into the oven and let the dough rise for 30 minutes. At the end of rising process, the dough should have risen past the top of the pan. If it needs a few more minutes to do so, wait another 5 minutes.
Remove the plastic wrap. Keep the loaf pan on the middle rack in the oven while the oven is preheating at 350°F. Bake for 50 minutes after the oven reaches 350°F.
Allow the loaf to cool in the pan for 5 minutes until it can be removed from the pan easily. Cool completely on a wire cooling rack before slicing.
Mix coconut milk and sugar in a bowl and drizzle on top of the peach cobbler bread before serving.