Preheat the oven to 350°F.
In a small bowl, mix the ground flax seeds and the water and let it rest 5 minutes.
In a large bowl, mix all the dry ingredients together.
In a second large bowl, whisk together the oil, the sugar and the flax seeds mix.
Microwave the peanut butter for 30 seconds and add it to the other liquids. Add the vanilla extract and the soy milk and whisk again until the volume expands slightly, about 2 minutes.
Using a spatula, gradually incorporate the dry ingredients into the wet. Add the mini eggs and mix one more time.
Using your hands, use about 2 tablespoons of cookies dough to form small balls and place them on a baking sheet covered with parchment paper. Press them down to make the cookies about 1 cm thick.
Bake for 15 minutes or until the edges become slightly golden-brown.