Preheat your oven to 350 degrees F. Line your baking sheet with parchment and lay the two spaghetti squash halves cut side down. Transfer to the oven to roast for 20 to 25 minutes.
Remove and allow to cool for a few minutes. When cool enough to handle, scoop out the seeds and discard. Using the tines of a fork, scrape the strands of spaghetti squash flesh and transfer them to a bowl. Repeat with the other half. Mix in the zested garlic clove, 1/2 teaspoon salt and pinch of pepper.
Generously grease a muffin tin, by using spray or rubbing each cup with an olive oil-dipped paper towel, and set aside.
Spoon about 2 tablespoons of butternut squash strands into each muffin cup, being sure to line the bottom and the sides. I found it helpful to use a small spoon to press the bottom and sides; you definitely want the spaghetti squash tightly packed. Crack an egg into each muffin cup. (Note: I found large eggs to have about a teaspoon too much of egg white so I cracked the egg in but didn't put in all of the egg white. This helped with the look of them.)
Transfer the muffin tin to the oven and bake for 10 to 12 minutes, until the whites are set, but yolks still appear soft. Allow the egg baskets to cool in the pan for 2 minutes. Run a sharp paring knife around the edges of each basket and gently remove it. Top with a few pinches of pepper, salt and some chives or chive flowers.