Preheat the oven to 400 degrees F. Spread the chopped carrots, parsnip, and sweet potato over a large baking sheet. Drizzle with olive oil and sprinkle with sea salt and Italian seasoning (or seasonings of choice). Use your hands to toss everything together so that it is well coated.

Place the chopped beet on a long sheet of foil and wrap the chunks in a foil packet (make sure the foil packet is nice and secure, because beet juices will begin to seep out while roasting). 

Place both the sheet of vegetables and the foil packet in the preheated oven. Roast 20 minutes, stir the vegetables on the tray, and roast an additional 10 minutes. Remove the tray from the oven and allow the beet to continue roasting another 10 minutes, or until beet chunks are very tender and juicy.

Add the ingredients for the avocado hollandaise sauce to a blender and blend until completely smooth. Taste for flavor and add more salt, cayenne, and/or vinegar to taste. For thinner consistency, add more water.

Fill a pot with a couple inches of water and bring it to a full boil. Reduce the heat to a gentle simmer (water should be steamy but not bubbly) and add a splash of white vinegar. Crack an egg into a small bowl or ramekin, then gently transfer it to the hot water. Use a slotted spoon to gently bring the whites toward the yolk in order to keep the egg together. Remove from heat, cover, and allow egg to cook 3 to 4 minutes. Use a slotted spoon to gently lift egg out of the water. Repeat for remaining eggs.