Preheat oven to 375°F (190°C).
Sauté fresh spinach in a small pan with 1 teaspoon of olive oil until wilted; drain all excess moisture thoroughly.
Butterfly each chicken breast by slicing horizontally through the middle, stopping before cutting all the way through to create a pocket.
Season the interior and exterior of the chicken breasts with salt, black pepper, and smoked paprika.
Fill each pocket with equal portions of sautéed spinach and shredded mozzarella cheese; secure the edges with toothpicks.
Heat the remaining olive oil in an oven-safe skillet over medium-high heat and sear the chicken for 3 to 4 minutes per side until golden brown.
In a small microwave-safe bowl, combine butter, minced garlic, and honey; heat until melted and whisk to combine.
Brush half of the garlic butter glaze over the seared chicken breasts.
Transfer the skillet to the oven and bake for 10 to 12 minutes, or until the internal temperature reaches 165°F (74°C).
Remove from oven, brush with remaining glaze, and let rest for 5 minutes before removing toothpicks and serving.