Melt the butter in a large pot or Dutch oven over medium heat. Add the leeks, 3/4 teaspoon of the salt, and several grinds of pepper and cook, stirring occasionally, for 8 to 10 minutes, or until the leeks are soft. If the leeks start browning before they soften, reduce the heat.

Add the asparagus, garlic, broth, and thyme and simmer for 20 minutes, or until the asparagus is tender. Add the peas and cook for 2 more minutes, or until heated through.

Remove from the heat and allow to cool slightly. Remove the thyme, then transfer the soup to a blender and blend until smooth. Return the soup to the pot and stir in the remaining 1/2 teaspoon salt, the lemon juice, and cream, if using. Season to taste.

Portion into bowls and top with a drizzle of cream, sautéed asparagus tips, and fresh dill. Drizzle with olive oil, garnish with freshly ground black pepper, and serve.