Heat the olive oil in a large stock pot. Add the onions and sauté for 3-5 minutes on high heat. Then reduce the heat to medium and allow the onions to cook slowly for 20-25 minutes, stirring occasionally until they are richly browned. If the onions start to char or sizzle, the heat is too high.
Add the garlic, carrots, celery and and spices. Stir to coat and sauté for an additional 5-7 minutes until the vegetables start to soften and begin to brown. Add the cut cauliflower and Yukon gold potatoes. Stir to coat.
Add the vegetable broth, reserving 1 cup, and the coconut milk. Bring to a simmer.
While the broth is simmering, add the reserved vegetable broth and 1 cup of water to a small stockpot. Add the carrots, celery and Yukon Gold potatoes from the Chunky Vegetables portion of the recipe. Simmer until the vegetables are soft enough to eat.
Prepare the mushrooms in a skillet with ¼ cup of water. Bring to a simmer and continue to cook until the water has cooked off. Add a teaspoon of olive oil and cook until the mushrooms are gently browned.
When the vegetables in the broth have become soft, puree the broth with an immersion blender. Season with salt and pepper to taste. Add the chunky vegetables with the reserved vegetable broth and water, the mushrooms and the cup of peas. Stir to combine and heat until the peas are warmed through.