Preheat the oven to 375°F (190°C). Lightly coat a baking dish with cooking spray.
Arrange the baby spinach in an even layer across the bottom of the prepared baking dish.
Sprinkle about half of the grated Fontina cheese evenly over the spinach.
Carefully crack the eggs over the spinach and cheese, spacing them evenly throughout the baking dish.
Season the eggs with coarse kosher salt and freshly ground black pepper. Drizzle the heavy cream or half-and-half over the top.
Sprinkle the remaining Fontina cheese over the eggs.
Bake for 15–25 minutes, depending on your preferred egg consistency. Check frequently toward the end of the cooking time so the yolks reach your desired doneness.
Meanwhile, melt the butter in a small saucepan over medium heat. Once it begins bubbling, whisk continuously until small golden-brown bits form at the bottom.
Remove the browned butter from the heat and continue whisking for about 30 seconds. Allow it to rest for 2 minutes.
Whisk in the minced garlic, then stir in the panko breadcrumbs until evenly coated.
When the Cheesy Spinach Baked Egg Sandwiches filling is finished baking, remove the dish from the oven. Sprinkle the garlic breadcrumbs and chopped parsley over the eggs.
Scoop one baked egg with plenty of spinach and melted cheese onto each toasted whole grain ciabatta roll. Serve warm.