Combine potatoes and water in a pot and bring to a boil, heavily season with salt, cook until very tender, strain and place back into the pot. Add yogurt and butter and mash with a potato masher until smooth.
Preheat oven to 400°F.
In a cast iron pan or oven-safe pan, heat the olive oil on medium heat. Cook the onions until golden, about 5-7 minutes. Reduce heat to low, add the garlic, mushrooms, carrots and thyme, and cook until the vegetables soften, about 5 minutes.
Add tomato paste and quinoa, cook until the tomato paste begins to stick to the vegetables. Then add the vegetable stock and peas and stir to combine. Carefully place mashed potatoes on top of the filling.
Place the pie in the oven on the middle rack and bake until the potatoes begin to brown, about 25-30 minutes, then broil for 2-3 minutes until the potatoes become golden. Remove from the oven and let stand for 10 minutes. Sprinkle with fresh herbs before serving.