Wash and peel the potato, carrots, and chayote squash, reserving the peels. In a medium pot, combine the peels with one half liter of water, half of the onion, 1 minced garlic clove, and salt to taste. Boil for 5 minutes. Strain. Discard the peels, reserving the broth. Set aside.
Finely dice the carrots, squash, and green beans. Place in a medium pot, cover with water and boil for 2 minutes. Dice the potato and zucchini and add to the pot. Boil for an additional 15 minutes. Remove from heat and set aside.
Clean mushrooms by removing the thin skin from the tops and cutting off the ends of the stems. Slice mushrooms. Heat a small amount of the grapeseed oil in a skillet over medium heat. Add sliced mushrooms and sauté until lightly brown. Remove from heat. Set aside.
Heat a small amount of the grapeseed oil in a skillet over medium heat. Add the remaining diced onion and sauté for few minutes. Stir in remaining minced garlic, sauté for a few more minutes and add the diced tomatoes. Sauté until well cooked. Salt to taste. Remove from heat, allow to cool. Transfer to a blender. Add the chili and cilantro. Blend until liquified.
In a large soup pot, combine the blended mixture with all the reserved ingredients: broth from the peels, cooked vegetables with their liquid, and cooked mushrooms. Add chickpeas and corn kernels. Bring to a boil and cook for 3 minutes. Remove from heat.
Serve hot, garnished with lemon slices and avocado slices.