For the Gougere: Heat oven to 400°F. Line baking sheet(s) with parchment paper. Set aside.
Place milk, butter, salt, and sugar in a saucepan. Bring to boil. Remove from heat and add flour all at once. Whisk until mixture comes together in a mass (it will be sticky). Add any dough clinging to whisk to mass. Over medium heat, stir the dough, breaking it up and bringing it back together for a couple minutes.
Transfer dough to a bowl of stand mixer with paddle attachment. Add eggs one at a time, combining until smooth after each addition and scraping down sides of the bowl. Mix in Le Gruyère cheese and a few cranks of black pepper.
Scoop dough into a piping bag. Pipe into 2-inch balls, placing them 2 inches apart, on prepared baking sheets. Dip your fingers or thumb in water and tap tops of dough balls with a wet finger. Grate additional Le Gruyère over gougère tops.
Bake 15-20 minutes. Reduce oven heat to 350°F; rotate baking sheets and bake additional 25-30 minutes. Remove from oven. Transfer grougères to cooling racks.
For the Creamed Spinach: Set a large sauté pan on medium-high heat. Add the butter and the garlic and let the garlic sizzle just for a few seconds.
Add spinach and salt and cream and toss just as the cream starts to come to a simmer. Remove spinach from the cream with tongs and add to a blender. Add the applesauce, nutmeg and parsley to the blender. Pour in the cream and puree. Taste and add salt as needed.
For the Le Gruyère Chive Scrambled Eggs: In a large frying pan on low heat, add the butter. Whisk the eggs together with a fork or whisk in a bowl. When the butter is almost all melted, add the eggs and gently cook for a minute, push the eggs from the edges of the pan inwards with a wooden spoon or spatula and season with salt and pepper and chives.
Cook another minute or so and give it another push from the sides. Add the grated cheese and fold gently until eggs are cooked soft. Add some fresh ground pepper.
To Serve: Warm the gougere as you are cooking the eggs. Spoon some warmed creamed spinach in the middle of each plate. Split the gougere in half as to make a “sandwich”. Set bottom half on each pool of creamed spinach. Spoon scrambled eggs into each gougere and top with the other half. Serve warm.