Heat the olive oil in a large saucepan over medium-high heat. Add the onion, garlic, and thyme, reduce the heat to medium-low, and cook until the mixture is soft and fragrant, about 3 minutes stirring occasionally.
Stir in the tomato paste and cook while stirring constantly until the tomato paste darkens, 1 1/2 to 2 minutes. Add the canned tomatoes and their juices and simmer, stirring occasionally until slightly thickened and reduced, about 7 minutes.
Remove the thyme sprigs and discard. Transfer the mixture to a Vitamix blender, mix on low. Pour in the broth/stock, almond milk, and yogurt and blend gently until completely smooth.
Pour the soup back into a clean pot and cook over medium heat until it’s warm, about 5 minutes. Stir in the sea salt.
Serve with a dolop of yogurt and some chopped fresh basil if you have some in the fridge.