Heat the olive oil in a large pot over medium heat. Add the onion and cook for 3 minutes until it softens.
Stir in the garlic and thyme. Cook for 1 minute until fragrant.
Add the mushrooms and cook for 5 minutes, stirring now and then, until they release their liquid.
Pour in the vegetable broth and add the rinsed kamut. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 45 minutes until the kamut is tender.
Stir in the chopped roasted peppers, salt, and black pepper. Simmer uncovered for 5 more minutes.
Ladle the soup into bowls and top each serving with fresh parsley.