For the eggs: Add some drops of the food coloring to a small zip-top bag. Mix to combine.
Lightly tap the eggs on a hard surface; be gentle, you want the shells crack but not peel off. Put the eggs in the zip-top bags and rub them around to coat with food coloring. Let sit for at least 2 to 3 hours in the refrigerator. You can make this overnight and have them ready for breakfast. Remove the eggs from the bag, rinse them off and remove the shells.
For the nest: Preheat the oven to 425 degrees F.
Bake the potatoes until almost tender, about 30 minutes. Allow to cool, then peel and grate them. Season with salt and pepper.
Using cooking spray, generously coat 6 muffin cups. Divide the grated potatoes among the muffin cups. Use your fingers to gently press the sides and bottom in each muffin cup to make a nest. Bake until golden brown, 15 to 20 minutes.
To serve, start with 1/2 cup of baby spinach leaves on each plate, put the sweet potato nest on top and 1 egg inside each nest.