Preheat oven to 425 degrees F (220 degrees C).
In an 8- or 9-inch cast-iron or oven-going skillet heat Olive Oil (2 tablespoon) over medium heat. Add the Garlic (1 clove); cook 3 to 4 minutes or until golden brown, turning occasionally. Remove the garlic; finely chop and set aside.
Add the Breadcrumbs (1/2 cup) to the skillet; cook 4 minutes or until golden. Transfer to a small bowl; stir in the chopped garlic, 1/4 teaspoon Salt (to taste) and 1/8 teaspoon Freshly Ground Black Pepper (to taste); let cool. Stir in the Shredded Parmesan Cheese (1/4 cup) and chopped Italian Flat-Leaf Parsley (1 tablespoon).
Cut the Delicata Squash (1 pound) into four 1 3/4- to 2-inch-thick rings. Using a spoon or melon baller, scoop out the seeds and flesh to create a 1 1/2- to a 2-inch-diameter hole.
Wipe the skillet. Add the remaining Olive Oil (1 tablespoon). Add the squash rings, turning to coat all sides with oil. Sprinkle with 1/4 teaspoon of Salt (to taste) and toss in the Fresh Thyme (4 sprig). Bake for 15 minutes and flip the squash over.
Remove the thyme stems. Crack one of the Large Egg (4) into a small cup or bowl; slide it into a squash ring. Repeat with the remaining eggs. Sprinkle the eggs with 1/4 teaspoon Salt (to taste) and 1/8 teaspoon Freshly Ground Black Pepper (to taste). Bake for 10 minutes more or until the egg whites are set.
Top with the breadcrumb mixture. If desired, garnish with fresh thyme sprigs. Serve immediately and enjoy!