Finely chop the garlic and green chiles, and scoop them into a bowl.
One at a time, run a knife down through each avocado, starting at the top, until you reach the pit; continue cutting around the pit until you reach the point you started.
Twist the two halves of the avocado apart. Remove the pit and discard. Scoop the flesh into the bowl with the chiles. Mash coarsely with the back of a spoon or an old-fashioned potato masher.
Add the herbs and onion, stir to combine, then taste. Season with salt (usually about a teaspoon) and lime juice. Scoop into a serving dish and garnish with cheese and radishes.