Heat olive oil in a large skillet over medium heat. Add chopped onion and minced garlic and sauté until the onion is translucent.
Add the ground chicken to the skillet. Cook and stir until browned and fully cooked.
Reduce heat, then pour in the heavy cream and stir to combine with the chicken.
Gradually add the grated Parmesan cheese, stirring constantly to create a smooth, creamy sauce.
Season the mixture with nutmeg, salt, and pepper. Cook for 2 to 3 minutes until the sauce thickens.
Preheat the oven broiler.
Split hamburger buns and place them on a baking sheet. Broil the buns for 1 to 2 minutes until lightly toasted.
Place spinach leaves on the bottom halves of the buns.
Spoon the chicken Alfredo mixture over the spinach layers.
Top each with shredded mozzarella cheese.
Broil again for 1 to 2 minutes until the cheese melts and bubbles.
Remove from oven, garnish with fresh parsley if desired, place the top bun halves over the mixture, and serve immediately.