Remove ends from radishes and wash with water. Slice radishes about 1/4" thick. (If using jicama, cut into about 1"x1" slices that are 1/4" thick).
Melt butter in non-stick pan at medium heat.
Once butter has melted add radish slices to the pan. Fry radishes uncovered on medium heat in butter 12-15 minutes, flipping them about 6 minutes in. (If using jicama you may need to cook longer for it to soften.)
Once cooked, remove radishes and lay across bottom of 8"x8" baking pan.
Using the same skillet as the radishes, reduce heat to medium-low and add garlic and chopped onions to pan. Cook for 2-3 minutes.
Add ground beef to the onions and add remaining seasonings and cook covered for 10-15 minutes, browning and crumbling with the spatula every few minutes as you go.
In a separate bowl mix sour cream and egg until thoroughly mixed.
Spread mixture on top of radishes in pan to cover the layer.
Once ground beef has finished cooking, spread ground beef in a layer on top of the sour cream layer.
Sprinkle cheddar cheese on top of ground beef.
Cook at 375F uncovered for 12-15 minutes.
Remove from oven. Let sit 5 minutes before serving.