Preheat the oven to 450°F.
Clean the beet roots and dice them into 1/2" pieces. Toss them with the cumin, 1/2 teaspoon of salt and about a tablespoon of olive oil. Spread on a baking sheet and move to the oven to roast.
Separate the beet stems from the leaves. Rinse the beet stems and dice them up. Also dice up a medium onion.
Add the diced beet stems and onion to a large sauté pan, and mix in a couple tablespoons of olive oil, a teaspoon of salt, and the coriander and red pepper flakes. Sauté them on medium-high heat until the mixture is soft and the onions are translucent. Expect about 10 minutes.
While the mixture sautés, prepare the greens. Roll stacks of greens and slice into 1/2" strips. Fill a salad spinner with water, put the sliced greens in the salad spinner basket and immerse in the water. Agitate, so any grit sinks to the bottom of the bowl. Remove the basket from the water and dump the water.
When the stems and onions are properly sautéed, add the beet greens to the pan in two or three batches. Add the next batch as the previous batch wilts and makes room.
Remove the roasted beet roots from the oven and lower the oven temperature to 375°F.
Spread the beet root and the crumbled feta over the sautéed onions, stems and greens. Then carefully arrange the eggs around the pan, cracking one at a time. Season the eggs with a sprinkle of salt and black pepper.
Place the pan in the 375°F oven and bake. The time required varies with the oven properties and how you like the eggs, but expect around 8-12 minutes. Start checking at 8 minutes. For creamy yolks, you need to remove the pan while there is still a little jiggle in the egg whites. Check once a minute until the eggs are ready.
Finish by spreading the fresh herbs or pesto over the dish, along with the diced avocado.