Preheat your oven to 375°F (190°C). Pound the chicken breasts to an even thickness so they cook uniformly, then season with salt and pepper.
Heat olive oil in a skillet over medium heat. Sauté the minced garlic until fragrant, about 30 seconds, then add the chopped spinach. Cook until wilted and bright green, about 2-3 minutes. Remove from heat and let cool slightly.
In a mixing bowl, combine the ricotta cheese with the cooked spinach mixture and shredded mozzarella, stirring until well incorporated.
Spread a generous layer of the ricotta-spinach mixture onto each chicken breast, then roll them up tightly, securing with toothpicks if needed.
Place the rolled chicken breasts seam-side down in a baking dish. Top each with a sprinkle of shredded cheese for a bubbly, golden crust.
Bake uncovered in the preheated oven for about 25-30 minutes, or until the cheese is melted and bubbly and the chicken is cooked through to an internal temperature of 165°F (74°C).
Remove the dish from the oven, let it rest for a few minutes, then carefully remove toothpicks and slice the roll-ups into rounds to reveal the spiraled layers of chicken, cheese, and spinach.
Serve warm, garnished with additional herbs or a drizzle of olive oil, and enjoy the creamy, crispy-textured slices.