Preheat oven to 200°C. Grease the muffin tin with oil or butter. Press a piece of baking paper into each hole so it extends above edges. Put grated kumara in a colander and squeeze out as much liquid as possible.
Transfer kumara to a bowl. Add salt, pepper, flour and 1 egg. Stir to combine. Put a generous spoonful of kumara mixture in each hole, spreading over base and up sides. Bake for 20-25 minutes or until lightly golden around edges.
Meanwhile, cook bacon in a non-stick frying pan over a medium heat, for 4-5 minutes or until slightly crispy. Drain bacon on paper towel.
Sprinkle the cheeses evenly over bases of each hash brown nest. Next, add a small dollop of tomato relish. Sprinkle ½ of the bacon and ½ of the chives between nests, then carefully break an egg over each. Sprinkle with remaining bacon and chives. Bake for about 20 minutes or until egg is set.