Cut poblanos in half lengthwise, and discard the seeds and membranes. Place poblano halves (skin sides up), tomatoes, and garlic on a foil-lined baking sheet. Broil for 12 minutes or until poblanos are blackened, turning the tomatoes once. Place the poblanos in a zip-top plastic bag, and seal. Let stand 10 minutes. Peel poblanos, tomatoes, and garlic.
Place the poblanos and garlic cloves in a food processor, and pulse until coarsely chopped. Combine the poblano mixture, tomato, avocado, parsley, juice, and salt in a bowl. Sprinkle with cheese and radishes. Serve with tortilla chips.