The poblanos, tomatoes, and garlic: Lay the poblanos, tomatoes, and garlic on a baking sheet and set 4 inches below a very hot broiler. Roast, turning every couple of minutes, until the chiles and tomatoes are soft, blistered, and blackened in spots and the garlic is soft, 12 to 13 minutes. Place the chiles in a bowl, cover with a towel, and let stand for 5 minutes, then wipe off the blackened skin. Pull or cut out the stems, seed pods, and seeds; rinse quickly to remove any stray seeds and bits of char. When the tomatoes are cool, peel off and discard their skins. Slip the papery skins off the garlic. In a mortar or food processor, make a coarse puree of the roasted garlic and poblanos (with both mortar and processor, it's best to start with the garlic, then add the poblanos); place in a large bowl. Chop the roasted tomatoes (for this recipe, it's best not to use any of the juice from the baking sheet) and add to the poblano mixture along with the parsley.

Finishing the guacamole: Cut the avocado lengthwise in half around the pit, twist the halves apart and remove the pits. Scoop out the flesh into the bowl with the flavorings. Using a potato masher or the back of a large spoon, coarsely mash everything together. Taste and season with salt, usually a scant teaspoon, then add enough lime juice to enliven all the flavors. Cover with plastic wrap, placing it directly on the surface, and refrigerate until you're ready to eat.

To serve, scoop into a decorative bowl or Mexican mortar, sprinkle with the queso anejo and stud with radish slices.