Melt 1 tablespoon butter in a large nonstick skillet over medium heat. Add leek; cook 3 minutes, stirring frequently. Stir in 3/4 cup broth and peas; bring to a boil. Partially cover, reduce heat, and simmer 5 minutes. Place 1 1/2 cups pea mixture, remaining 3/4 cup broth, 1 cup basil leaves, and oil in a blender, and process until smooth. Place pureed pea mixture in a large bowl. Add remaining pea mixture to pureed pea mixture, and stir to combine.
Melt 2 tablespoons butter in pan over medium-high heat. Add mushrooms and garlic; sauté 6 minutes or until mushrooms are tender. Stir in pea mixture, pasta, salt, and black pepper. Sprinkle chopped basil evenly over each serving.