In a medium mixing bowl, mash avocados with the juice of one lime. Mix in chopped tomato, cilantro, garlic, salt, and chili powder.
Cut onion into ½-inch (1 cm) slices. Carefully separate the layers into individual rings. On a wax paper–lined tray, lay out onion rings and fill each with guacamole. Place tray in freezer until solid (about one hour).
Add flour, beaten eggs, and panko bread crumbs to three separate bowls. Remove frozen guacamole rings from freezer. Roll each first in flour, then egg, then bread crumbs. Coat once more in egg and a final time in bread crumbs.
In a large saucepan, heat oil to 350˚F (180˚C). Fry guacamole onion rings in batches until nicely browned on all sides.
Place on paper towel–lined plate to drain off any excess oil. Sprinkle with salt and lime juice. Serve with sour cream.