In a large pot, melt the unsalted butter and olive oil over medium heat. Add the sliced leek and minced garlic, stirring until fragrant and softened, about 3-4 minutes.

Add the diced carrot, diced zucchini, chopped asparagus, and fresh or frozen peas. Stir and let cook for about 5 minutes until vegetables start to soften.

Pour in the vegetable broth, season with salt, pepper, and dried thyme. Bring to a gentle simmer, which should take around 5 minutes.

Allow the soup to simmer for 15-20 minutes until all vegetables are tender but not mushy.

Using an immersion blender, blend the soup until smooth and creamy or to your desired consistency.

Stir in the whole milk or plant-based milk, heavy cream or plant-based cream, fresh dill, and lemon juice, mixing well. Adjust seasoning as necessary.

Ladle the soup into warm bowls and garnish with fresh dill or chives if desired. Serve hot.