Preheat oven to 350, line two sheet pans with foil, and grease half of a muffin pan lightly with cooking oil. Set all pans aside.

Add spiralized sweet potatoes in large bowl and toss with olive oil, thyme, salt, and pepper.

Split potatoes between two sheet pans and spread in an even layer. Bake for 10-15 minutes, until lightly golden and softened. Remove from oven and let cool. Reduce temperature to 325.

While potatoes are cooking, heat a small sauté pan over medium heat, and add 1 tablespoon butter or ghee. Add sliced leeks, and season with salt and pepper.

Sauté leeks 10 minutes, or until lightly browned and softened, stirring often. Set aside to cool.

Once potatoes and leeks are cool enough to handle, toss them together to combine.

Divide potato and leek mixture evenly between muffin cups, forming a nest around the perimeter of each cup, leaving a hollow center.

Crack one egg into each cup, and place in 325 degree oven. Bake for 15-20 minutes or until whites are just barely set, the yolks will still jiggle.

Let cool a few minutes in the pan, then pop the nests out with a spoon. Top with chopped thyme, salt, and pepper and serve immediately.