In a soup pot on medium high heat, melt the butter and oil; add the onion, garlic and salt, and cook, stirring, for three minutes. Add the cherry tomatoes, artichokes, basil and oregano, and cook for an additional five to seven minutes; add the vegetable stock and bring to a simmer. Simmer for 15 minutes.
Blend the soup to your desired consistency with a hand blender.
To finish the soup, stir in the coconut milk.
To serve garnish the soup with fresh parmesan and thyme leaves.