Heat oil in a large Dutch oven over medium-high heat. Add onion and next 3 ingredients; sauté 5 minutes or until tender.
Add tomatillos and next 3 ingredients to pan; bring to a boil. Cover, reduce heat, and simmer 23 minutes, stirring occasionally. Remove from heat; cover and chill 1 1/2 hours.
Place avocado and half of soup in a blender; process until smooth. Transfer to a large bowl. Place remaining soup and cilantro in blender; process until smooth, and add to bowl. Stir in lime juice. Ladle soup into bowls; top with Tomato Salsa.