Trim the woody ends off the asparagus. Place on a sheet pan. Drizzle with 1 tablespoon olive oil, season with 1 teaspoon salt and ½ teaspoon pepper. Toss to coat, and roast for 10 minutes or until tender. Cut into 1-2 inch pieces, saving a few of the tips for garnish.
Clean the leeks and chop the white and light green parts. Heat 2 tablespoons oil in a stock pot or Dutch oven over medium heat. Add the leeks and cook, stirring occasionally, for 5 minutes. Add the garlic and cook, stirring occasionally, for another minute.
Save a few of the peas for garnish and place the rest in the pot along with the asparagus, vegetable broth, coconut milk, 1 teaspoon salt, and ½ teaspoon pepper. Raise the heat and bring to a boil. Pour the mixture into a blender, working in batches if necessary, and blend until smooth. Pour the mixture back into the pot, heat until hot, and stir in the tamari and lemon juice. Season to taste with additional salt and pepper, if necessary.
Serve, garnished with reserved asparagus tips and peas.